GEOMETRIC ANALYSIS O F RADIAL BUCKLING MICHAEL H. GOLDBAUM,
M.D.
Chicago, Illinois AND M A R T I N SMITHLINE, M.D.,
THOMAS A. POOLE, M.D.,
AND HARVEY A. LINCOFF,
M.D.
New York, New York
This study presents mathematical anal ysis of the buckle created by the extrascleral silicone sponge and correlates its effect with clinical observations. 1 The ef fect of vitreous traction on buckles of various orientations has been proposed. 2 The mathematical analysis is concerned with tensional forces on the retina overly ing the buckle induced directly by the buckle. DERIVATION AND CALCULATIONS
Excluding abnormal chorioretinal adhe sions, the retina adheres firmly to the coats of the eye at the ora serrata and at the disk margins. The distance of the retinal arc at radius 11.8 mm, between disk mar gin and ora is approximately 30.7 mm temporally, 25.5 mm nasally, and 29.3 mm superiorly and inferiorly (average disk to ora, 29 mm). These values are derived from average arcs at the scierai surface at 12.5-mm radius 3 / 11.8 I 32.5 mm X = 30.7 mm. \ 12.5 27 mm X 31 mm X
11.8 12.5 11.8 12.5
The circumference of the retina in the equa torial region is about 74.3 mm (r = 11.8 mm). The tension vectors along the sur face of the retina at any one point can be reduced to spherical coordinates at 90° to each other. ' In the sclera, we placed the mattress su tures over the expiant at a distance that approximates half the circumference of the cylindrical sponge. Consequently, a 5-mm sponge is held in place by mattress sutures 8 mm apart (a 4-mm sponge, held 6.5 mm apart, and a 3-mm sponge, held 5 mm apart). 1 Experimental evidence by one of us (H.A.L., unpublished data) with rab bits showed that with this expiant suture technique (Fig. 1), the sponge resumes its original diameter after some hours of equi libration, and the sclera is applied to half the circumference (Fig. 2, top). Thus, the length of the sclera in contact across a 5-mm sponge is or = fπ = 7.85 mm, where c = radius of sponge. However, the sclera and choroid have a combined thick ness in the equatorial region of approxi-
= 25.5 mm, = 29.3 j .
From the Department of Ophthalmology, Univer sity of Illinois Eye and Ear Infirmary, Chicago (Dr, Goldbaum), and the Department of Ophthalmology, New York Hospital-Cornell University Medical Center, New York, New York (Drs. Smithline, Poole, and Lincoff). Reprint requests to Michael H. Goldbaum, M.D., Fig. 1 (Goldbaum, Smithline, Poole, and Lincoff). Department of Ophthalmology, University of Illinois A 5-mm cylindrical silicone sponge sutured in meridi Eye and Ear Infirmary, 1855 W. Taylor St., Chicago, onal orientation with mattress sutures placed 8 mm IL 606I2. apart (about one half circumference of sponge). 958
RADIAL BUCKLING
VOL. 79, NO. 6
mately 0.7 mm,* which must be added to the sponge radius to calculate the length of the retina across the sponge. Further more, the retinal pigment epithelium (RPE) extends an arc across the buckle
959
less than 180° because of the thickness of the sclera and choroid at each end. Consequently, the length of RPE across the buckle on which the retina must settle is (c + α)π — 2a, where a = thickness of
Sclera
Choroid
Sclera Choroid RPE-Λ
r+a = l2.5
a=0.7
r=ll.8
Fig. 2 (Goldbaum, Smithline, Poole, and Lincoff). Top, A 5-mm sponge is sutured onto sclera shown in cross section. Note that sponge has resumed circular shape. To calculate the length of the retinal pigment epithelium (RPE) arc across the sponge (h to »'), the thickness of the sclera and choroid (a) must be added to the radius of the sponge (c). The arc h to i is less than 180° (* radians) by the thickness of the choroid and sclera {a/if + a) radians) at each end. Bottom, A 5-mm sponge is in contact with a scierai arc of 7.8 mm. Before buckling, the RPE under a 7.8-mm arc was only 7.4 mm.
AMERICAN JOURNAL OF OPHTHALMOLOGY
960
JUNE, 1975
TABLE 1 STRETCHING OF RPE ACROSS BUCKLE
Radius of sponge =c Arc of sclera in contact perpendicular to sponge (mm) Increase in RPE length perpendicular to sponge (mm)
sclera plus choroid; or (f + 0.7)x — 1.4 = 8.65 mm for a S-mm sponge. Before the buckle placement (Fig. 2, bottom), the length of the RPE was r+ a
X 7.85
11.8 X 7.85 = 7.4 mm, 12Ü where r = radius of RPE and (r + a) = radius of the outer surface of the eye ball. After a 5-mm sponge placement, the distance the retina must span is increased by about 1.3 mm in the meridian perpen dicular to the long axis of the buckle. The amount the RPE is stretched perpendicu lar to a 4- or 3-mm sponge is 1.2 and 1.1 mm (Table 1). We calculated the distance of the RPE along the longitudinal axis of the buckle by assuming that the ends of the buckle approximate the shape of a quarter seg ment of a sphere (Fig. 3, top). The distance from d to e is Θ — e) 360°
where r = radius of the retina and c = radius of the cylindrical sponge. The distance from/ to d is f to d =
(c + a)ir 2
2.0 mm
1.5 mm
7.8 1.3
6.3 1.2
4.7 1.1
Therefore, the length of the RPE along the length of the buckle is Θ / to g = (e + α)π — 2a + 2w(r — c) 360° The length of the RPE before the buckle was placed, however, was
or
d to e = 2Έ{Τ
2.5 mm
a
where a = thickness of sclera plus choroid. This distance also represents e to g. Thus, / to d + e to g = (c + a)ir — 2a.
2?rf
Θ r 1- 2(c + d) 360° r+ a
The point at which these two values be come equal is when T(C+O)
Θ = 360°
— 2a—2(c+a) r+a 2 ire
If a = 0.7 and c = 2.5 then Θ = 60°. For 4-mm and 3-mm sponges, tension is zero along the long axis when Θ = 57° and 52°. Denning buckle length a s / to g (Fig. 3), the corresponding arc angle Φ is approxi mated by Φ= Θ
2(c + a) 360° 2π(τ + a)
The buckle arc length Φ when tension reaches zero is 90°, 82°, and 72° for 5-, 4-, and 3-mm sponges (Table 2). Surface area of the buckle—One of the possible shapes of a torus is a doughnut shape. As the cylindrical sponge curves about the globe, it creates a buckle where the retina approximates the shape of the inner half of a torus. The surface area of the inner half of a torus is represented by the following equation : Area of shaded square dA = (c + a)d*-sd®
VOL. 79, NO. 6
RADIAL BUCKLING
961
Fig. 3 (Goldbaum, Smithline, Poole, and Lincoff). Top, Section along the long axis of a cylindrical sponge buckle. The shape of the ends of the buckle are a 90° section of a sphere. Φ represents the arc length of the buckle on the sclera. Bottom, As the cylindrical sponge curves about the globe, it creates a buckle where the RPE approximates the shape of the inner half of a torus. Note that angle Φ is less than 180° (jr radians) by the thick ness of the sclera and choroid (a) at each end (a/(e + a) radians). (Fig. 3, bottom). Integrating this, we finish with A =
360c WM
(c +
" 0 J n
The thickness of the sclera and choroid (a) must be added to the radius of the sponge (c) in this equation. The R P E across the sponge extends less than 180° (x radians), represented by
- N Cos *)dVd@ * =
where M = (c + a)2 + (r + a) 2 N = ψ =
2(r+a)(c+a) v
a
2
c+a
& Θ = 0 to 360°.
ir
a
2
c+ a
This complex integral is solved by numeri cal evaluation in steps of
, ■φ =
v
from Ψ = 0 to 200 2
v
a c+ a
962
AMERICAN JOURNAL OF OPHTHALMOLOGY
JUNE, 197S
TABLE 2 ARC LENGTH WHEN TENSION CHANGES TO COMPRESSION
Radius of sponge =c Θ when tension=0 along long axis of buckle Φ= arc length of buckle when tension is zero
We programmed a DEC PDP11 computer using BASIC language, and obtained a printout with (c + a) and (r — c) as the variables. The RPE area overlying the sponge (neglecting the sloping ends at present) is then compared to the area of the zone of RPE (at radius 11.8 mm) whose width, prior to buckle placement, was arr/ix + a), or the projection at r (the ra dius of the RPE) of half the circumference of the sponge at the scierai surface (radius r + a). Comparing the surface area of the RPE after buckle placement to the same RPE prior to buckle placement, we found that the surface area of the RPE on the buckle is increased for any buckle length 0° to 360° (neglecting the sloping ends). Assuming that the sloping ends of a buckle less than 360° approximate a 90° segment of a sphere whose radius is c + a, the area on each sloping end would be w(c + a) 2 — wa(c + a). Prior to buckle placement, the RPE area at each end was
2.5 mm
2.0 mm
1.5 mm
60° 90°
57° 82°
52° 72°
limbal-parallel buckle elongates the dis tance between the disk and ora by about 1.3 mm with a 5-mm diameter sponge. A certain amount of elasticity may be ex pected in the retina. When this elasticity is exceeded, the retina accommodates this greater disk-to-ora distance in either of two ways: a transient concave detach ment may form posterior to the buckle (Fig. 4), or the retina under certain circum stances may tend toward a chord, resulting in a meridional fold off the buckle (Fig. 5). The retinal circumference along the equator is 74.3 mm, more than double the distance of the retinal arc from disk to ora which averages 29 mm. Consequently, if the buckle is placed meridionally, the per centage increase by the buckle of the RPE length along the equatorial circumference
-χ(—Y2
V -t- a/
The RPE area of each sloping end ex ceeds the RPE area occupied by the slop ing ends prior to buckle placement. The total result is that for buckles less than 360° (and thus sloping ends) and for full 360° buckles, the RPE area increases with buckle placement. This means that stretch ing across the buckle more than compen sates for compression along the long axis of a long buckle. DISCUSSION
Effect of tension forces on the retina—EF Fig. 4 (Goldbaum, Smithline, Poole, and Lincoff). OF LIMBAL-PARAIXEL BUCKLE—The Concave detachment posterior to the buckle.
FECT
VOL. 79, NO. 6
RADIAL BUCKLING
963
1.3 m m \ . J is less than half the percent( 74.3 mm> / age increase of the RPE between disk and ora across a limbal-parallel buckle Ί . 3 mm\ Thus, the elasticity of the < 29 mm/ ' retina over a radial buckle is less likely to be exceeded. EFFECT OF TENSION ACROSS BUCKLE ON HORSESHOE TEAR—We have considered a
point in the anterior equatorial zone of the retina near the 12 o'clock meridian (Fig. 6, A). If we increase the anteroposterior tension, we might expect the retina to dis tort slightly according to the elasticity of
Fig. 5 (Goldbaum, Smitbline, Poole, and Lincoff). Buckle (b) of a limbal-parallel orientation and a retinal fold (rf) extending off the buckle through the macula (m) to tbe disk.
Fig. 6 (Goldbaum, Smithline, Poole, and Lincoff). A, A point in the anterior equatorial retina at 12 o'clock with tensional forces broken down into anterior, posterior, nasal, and temporal vectors. B, Horseshoe tear at 12 o'clock in anterior equatorial zone of retina. Note that if force is applied at the posterior edge of the tear or at the base of the flap, the force is unopposed allowing distortion of the tear. C, Distortion produced by anteroposterior tension across a limbal-parallel buckle elongates the opening of a horseshoe tear in the anteroposterior meridian, causing fishmouthing and persistent detachment. D, Meridional orientation of buckle prevents fishmouthing off posterior edge of horseshoe tear.
964
AMERICAN JOURNAL OF OPHTHALMOLOGY
JUNE, 1975
before the buckle was placed. The retina then tends to make folds on the buckle. This is a consequence of negative tension, or compression, along the length of the buckle. Although the retina may, as its elasticity allows, stretch slightly under positive tension, it does not compress but rather forms folds since the retina cannot support a bending moment (Fig. 7). Note that the folds generated by compressional forces along the length of a buckle are on the buckle, whereas the folds generated by tensional forces across a buckle are off the buckle. Compression folds on a 5-mm sponge begin to appear around 90° arc length. The stretching across a buckle and the Fig. 7 (Goldbaum, Smithline, Poole, and Lincoff ). A long limbal-parallel buckle produces folds of retina compression along a long, limbal-parallel on the buckle by compressing the retina, which can buckle are disadvantageous when a long, not support a bending moment. limbal-parallel buckle is used for a large retinal tear. Meridional folds of the pos the retina. Consider a horseshoe tear at terior edge of the tear are almost sure to 12 o'clock in the anterior equatorial zone form. E F F E C T OF INCREASED SURFACE AREA (Fig. 6, B). As the anteroposterior tension increases (as with a limbal-parallel buckle), OVER A BUCKLE—The effect of increased there is no opposing anterior tension to retinal surface area over a buckle is not posterior tension a t the posterior edge of clear. I t may explain the tendency of com the horseshoe tear, and no opposing pos pression folds on a long buckle to iron out terior force to anterior tension a t the in time. base of the flap, except perhaps from the SUMMARY vitreous, transmitted through the flap. The result is an anteroposterior elonga Tension analysis along the retinal sur tion of the tear, producing fishmouthing face demonstrates the advantage of meridi (Fig. 6, C). onal buckles over limbal-parallel buckles. A meridionally placed sponge will pro A cylindrical sponge generates tensional duce naso temporal tension, but less than forces in the retina along the long axis of half the anteroposterior tension produced the buckle and perpendicular to it. The by a limbal-parallel sponge. This smaller tension perpendicular to the sponge is nasotemporal tension from a meridional positive, and the retina and retinal pig sponge should distort the tear less (Fig. 6, ment epithelium stretch in that direction. D) ; in fact, we have never seen a fishmouth The tension along the long axis is positive laterally from a retinal break over a me (stretching) when the buckle is less than 90° arc length ; and negative (compression), ridional sponge. greater than 90° for a 5-mm sponge. Con EFFECT O F A LIMBAL-PARALLEL SPONGE GREATER THAN 90°—When a sponge whose sequently, retinal compression folds on the arc length is greater than 90° is placed, the buckles occur for buckles of arc length retina must fall on R P E which is shorter greater than 90°. These tension forces a t along the buckle's long axis than it was right angles to each other explain the de-
VOL. 79, NO. 6
RADIAL BUCKLING
velopment of (1) concave retinal detach ment or retinal folds off short limbal-parallel buckles, (2) retinal folds on long limbalparallel buckles, and (3) fishmouthing of horseshoe tears overlying a limbal-parallel buckle. The buckle increases retinal surface area overlying the buckle. The significance of this is not clear, but it may explain the lessening or disappearance of compression folds on the buckle in time.
965
New Orleans, for his advice in the derivation of the surface area of the buckle.
REFERENCES
1. Lincoff, H. A., and Kreissig, I.: The rationale for radial buckling. Am. J. Ophthalmol. 179: 955, 1975. 2. Meyer, H.: Meridional versus equatorial and latitudinal buckles in retinal detachment surgery. S. Afr. Med. J. 44 (Suppl.): 21, 1970. 3. Stallard, H. B.: Eyè Surgery, 4th ed. Bristol, John Wrigles and Sons Ltd., 1965, p. 699. 4. Hogan, M. J., Alvarado, J. A., and Weddell, ACKNOWLEDGMENTS J. E.: Histology of the Human Eye. Philadelphia, We thank Lyle Ferguson of T.A.N.O. Corporation, W. B. Saunders, 1971, pp. 187 and 328.
HERMAN M. BURIAN, M.D. 19061974 The dissemination of information about new books is a prime task of any periodical publication. This task can be fulfilled by appropriate publicity inserted by the publisher. More informative are—or should be—reviews of books by competent reviewers. Book reviews in ophthalmic publications are frequently disappointing. A review which simply lists the table of contents and concludes with à laudatory sentence tells the reader no more than the publisher's blurb or advertisement. The occasional humorous review of a serious book— making the author the straight man for some clown in the sticks, or the big city for that matter—is an injustice to the author and the readers. The usual polite reviews which quite obviously steer clear of any criti cal comment are of little use to the readers. On the reviewing of books Am. J. Ophthalmol. 66:756, 1968
M.D.
Chicago, Illinois AND M A R T I N SMITHLINE, M.D.,
THOMAS A. POOLE, M.D.,
AND HARVEY A. LINCOFF,
M.D.
New York, New York
This study presents mathematical anal ysis of the buckle created by the extrascleral silicone sponge and correlates its effect with clinical observations. 1 The ef fect of vitreous traction on buckles of various orientations has been proposed. 2 The mathematical analysis is concerned with tensional forces on the retina overly ing the buckle induced directly by the buckle. DERIVATION AND CALCULATIONS
Excluding abnormal chorioretinal adhe sions, the retina adheres firmly to the coats of the eye at the ora serrata and at the disk margins. The distance of the retinal arc at radius 11.8 mm, between disk mar gin and ora is approximately 30.7 mm temporally, 25.5 mm nasally, and 29.3 mm superiorly and inferiorly (average disk to ora, 29 mm). These values are derived from average arcs at the scierai surface at 12.5-mm radius 3 / 11.8 I 32.5 mm X = 30.7 mm. \ 12.5 27 mm X 31 mm X
11.8 12.5 11.8 12.5
The circumference of the retina in the equa torial region is about 74.3 mm (r = 11.8 mm). The tension vectors along the sur face of the retina at any one point can be reduced to spherical coordinates at 90° to each other. ' In the sclera, we placed the mattress su tures over the expiant at a distance that approximates half the circumference of the cylindrical sponge. Consequently, a 5-mm sponge is held in place by mattress sutures 8 mm apart (a 4-mm sponge, held 6.5 mm apart, and a 3-mm sponge, held 5 mm apart). 1 Experimental evidence by one of us (H.A.L., unpublished data) with rab bits showed that with this expiant suture technique (Fig. 1), the sponge resumes its original diameter after some hours of equi libration, and the sclera is applied to half the circumference (Fig. 2, top). Thus, the length of the sclera in contact across a 5-mm sponge is or = fπ = 7.85 mm, where c = radius of sponge. However, the sclera and choroid have a combined thick ness in the equatorial region of approxi-
= 25.5 mm, = 29.3 j .
From the Department of Ophthalmology, Univer sity of Illinois Eye and Ear Infirmary, Chicago (Dr, Goldbaum), and the Department of Ophthalmology, New York Hospital-Cornell University Medical Center, New York, New York (Drs. Smithline, Poole, and Lincoff). Reprint requests to Michael H. Goldbaum, M.D., Fig. 1 (Goldbaum, Smithline, Poole, and Lincoff). Department of Ophthalmology, University of Illinois A 5-mm cylindrical silicone sponge sutured in meridi Eye and Ear Infirmary, 1855 W. Taylor St., Chicago, onal orientation with mattress sutures placed 8 mm IL 606I2. apart (about one half circumference of sponge). 958
RADIAL BUCKLING
VOL. 79, NO. 6
mately 0.7 mm,* which must be added to the sponge radius to calculate the length of the retina across the sponge. Further more, the retinal pigment epithelium (RPE) extends an arc across the buckle
959
less than 180° because of the thickness of the sclera and choroid at each end. Consequently, the length of RPE across the buckle on which the retina must settle is (c + α)π — 2a, where a = thickness of
Sclera
Choroid
Sclera Choroid RPE-Λ
r+a = l2.5
a=0.7
r=ll.8
Fig. 2 (Goldbaum, Smithline, Poole, and Lincoff). Top, A 5-mm sponge is sutured onto sclera shown in cross section. Note that sponge has resumed circular shape. To calculate the length of the retinal pigment epithelium (RPE) arc across the sponge (h to »'), the thickness of the sclera and choroid (a) must be added to the radius of the sponge (c). The arc h to i is less than 180° (* radians) by the thickness of the choroid and sclera {a/if + a) radians) at each end. Bottom, A 5-mm sponge is in contact with a scierai arc of 7.8 mm. Before buckling, the RPE under a 7.8-mm arc was only 7.4 mm.
AMERICAN JOURNAL OF OPHTHALMOLOGY
960
JUNE, 1975
TABLE 1 STRETCHING OF RPE ACROSS BUCKLE
Radius of sponge =c Arc of sclera in contact perpendicular to sponge (mm) Increase in RPE length perpendicular to sponge (mm)
sclera plus choroid; or (f + 0.7)x — 1.4 = 8.65 mm for a S-mm sponge. Before the buckle placement (Fig. 2, bottom), the length of the RPE was r+ a
X 7.85
11.8 X 7.85 = 7.4 mm, 12Ü where r = radius of RPE and (r + a) = radius of the outer surface of the eye ball. After a 5-mm sponge placement, the distance the retina must span is increased by about 1.3 mm in the meridian perpen dicular to the long axis of the buckle. The amount the RPE is stretched perpendicu lar to a 4- or 3-mm sponge is 1.2 and 1.1 mm (Table 1). We calculated the distance of the RPE along the longitudinal axis of the buckle by assuming that the ends of the buckle approximate the shape of a quarter seg ment of a sphere (Fig. 3, top). The distance from d to e is Θ — e) 360°
where r = radius of the retina and c = radius of the cylindrical sponge. The distance from/ to d is f to d =
(c + a)ir 2
2.0 mm
1.5 mm
7.8 1.3
6.3 1.2
4.7 1.1
Therefore, the length of the RPE along the length of the buckle is Θ / to g = (e + α)π — 2a + 2w(r — c) 360° The length of the RPE before the buckle was placed, however, was
or
d to e = 2Έ{Τ
2.5 mm
a
where a = thickness of sclera plus choroid. This distance also represents e to g. Thus, / to d + e to g = (c + a)ir — 2a.
2?rf
Θ r 1- 2(c + d) 360° r+ a
The point at which these two values be come equal is when T(C+O)
Θ = 360°
— 2a—2(c+a) r+a 2 ire
If a = 0.7 and c = 2.5 then Θ = 60°. For 4-mm and 3-mm sponges, tension is zero along the long axis when Θ = 57° and 52°. Denning buckle length a s / to g (Fig. 3), the corresponding arc angle Φ is approxi mated by Φ= Θ
2(c + a) 360° 2π(τ + a)
The buckle arc length Φ when tension reaches zero is 90°, 82°, and 72° for 5-, 4-, and 3-mm sponges (Table 2). Surface area of the buckle—One of the possible shapes of a torus is a doughnut shape. As the cylindrical sponge curves about the globe, it creates a buckle where the retina approximates the shape of the inner half of a torus. The surface area of the inner half of a torus is represented by the following equation : Area of shaded square dA = (c + a)d*-sd®
VOL. 79, NO. 6
RADIAL BUCKLING
961
Fig. 3 (Goldbaum, Smithline, Poole, and Lincoff). Top, Section along the long axis of a cylindrical sponge buckle. The shape of the ends of the buckle are a 90° section of a sphere. Φ represents the arc length of the buckle on the sclera. Bottom, As the cylindrical sponge curves about the globe, it creates a buckle where the RPE approximates the shape of the inner half of a torus. Note that angle Φ is less than 180° (jr radians) by the thick ness of the sclera and choroid (a) at each end (a/(e + a) radians). (Fig. 3, bottom). Integrating this, we finish with A =
360c WM
(c +
" 0 J n
The thickness of the sclera and choroid (a) must be added to the radius of the sponge (c) in this equation. The R P E across the sponge extends less than 180° (x radians), represented by
- N Cos *)dVd@ * =
where M = (c + a)2 + (r + a) 2 N = ψ =
2(r+a)(c+a) v
a
2
c+a
& Θ = 0 to 360°.
ir
a
2
c+ a
This complex integral is solved by numeri cal evaluation in steps of
, ■φ =
v
from Ψ = 0 to 200 2
v
a c+ a
962
AMERICAN JOURNAL OF OPHTHALMOLOGY
JUNE, 197S
TABLE 2 ARC LENGTH WHEN TENSION CHANGES TO COMPRESSION
Radius of sponge =c Θ when tension=0 along long axis of buckle Φ= arc length of buckle when tension is zero
We programmed a DEC PDP11 computer using BASIC language, and obtained a printout with (c + a) and (r — c) as the variables. The RPE area overlying the sponge (neglecting the sloping ends at present) is then compared to the area of the zone of RPE (at radius 11.8 mm) whose width, prior to buckle placement, was arr/ix + a), or the projection at r (the ra dius of the RPE) of half the circumference of the sponge at the scierai surface (radius r + a). Comparing the surface area of the RPE after buckle placement to the same RPE prior to buckle placement, we found that the surface area of the RPE on the buckle is increased for any buckle length 0° to 360° (neglecting the sloping ends). Assuming that the sloping ends of a buckle less than 360° approximate a 90° segment of a sphere whose radius is c + a, the area on each sloping end would be w(c + a) 2 — wa(c + a). Prior to buckle placement, the RPE area at each end was
2.5 mm
2.0 mm
1.5 mm
60° 90°
57° 82°
52° 72°
limbal-parallel buckle elongates the dis tance between the disk and ora by about 1.3 mm with a 5-mm diameter sponge. A certain amount of elasticity may be ex pected in the retina. When this elasticity is exceeded, the retina accommodates this greater disk-to-ora distance in either of two ways: a transient concave detach ment may form posterior to the buckle (Fig. 4), or the retina under certain circum stances may tend toward a chord, resulting in a meridional fold off the buckle (Fig. 5). The retinal circumference along the equator is 74.3 mm, more than double the distance of the retinal arc from disk to ora which averages 29 mm. Consequently, if the buckle is placed meridionally, the per centage increase by the buckle of the RPE length along the equatorial circumference
-χ(—Y2
V -t- a/
The RPE area of each sloping end ex ceeds the RPE area occupied by the slop ing ends prior to buckle placement. The total result is that for buckles less than 360° (and thus sloping ends) and for full 360° buckles, the RPE area increases with buckle placement. This means that stretch ing across the buckle more than compen sates for compression along the long axis of a long buckle. DISCUSSION
Effect of tension forces on the retina—EF Fig. 4 (Goldbaum, Smithline, Poole, and Lincoff). OF LIMBAL-PARAIXEL BUCKLE—The Concave detachment posterior to the buckle.
FECT
VOL. 79, NO. 6
RADIAL BUCKLING
963
1.3 m m \ . J is less than half the percent( 74.3 mm> / age increase of the RPE between disk and ora across a limbal-parallel buckle Ί . 3 mm\ Thus, the elasticity of the < 29 mm/ ' retina over a radial buckle is less likely to be exceeded. EFFECT OF TENSION ACROSS BUCKLE ON HORSESHOE TEAR—We have considered a
point in the anterior equatorial zone of the retina near the 12 o'clock meridian (Fig. 6, A). If we increase the anteroposterior tension, we might expect the retina to dis tort slightly according to the elasticity of
Fig. 5 (Goldbaum, Smitbline, Poole, and Lincoff). Buckle (b) of a limbal-parallel orientation and a retinal fold (rf) extending off the buckle through the macula (m) to tbe disk.
Fig. 6 (Goldbaum, Smithline, Poole, and Lincoff). A, A point in the anterior equatorial retina at 12 o'clock with tensional forces broken down into anterior, posterior, nasal, and temporal vectors. B, Horseshoe tear at 12 o'clock in anterior equatorial zone of retina. Note that if force is applied at the posterior edge of the tear or at the base of the flap, the force is unopposed allowing distortion of the tear. C, Distortion produced by anteroposterior tension across a limbal-parallel buckle elongates the opening of a horseshoe tear in the anteroposterior meridian, causing fishmouthing and persistent detachment. D, Meridional orientation of buckle prevents fishmouthing off posterior edge of horseshoe tear.
964
AMERICAN JOURNAL OF OPHTHALMOLOGY
JUNE, 1975
before the buckle was placed. The retina then tends to make folds on the buckle. This is a consequence of negative tension, or compression, along the length of the buckle. Although the retina may, as its elasticity allows, stretch slightly under positive tension, it does not compress but rather forms folds since the retina cannot support a bending moment (Fig. 7). Note that the folds generated by compressional forces along the length of a buckle are on the buckle, whereas the folds generated by tensional forces across a buckle are off the buckle. Compression folds on a 5-mm sponge begin to appear around 90° arc length. The stretching across a buckle and the Fig. 7 (Goldbaum, Smithline, Poole, and Lincoff ). A long limbal-parallel buckle produces folds of retina compression along a long, limbal-parallel on the buckle by compressing the retina, which can buckle are disadvantageous when a long, not support a bending moment. limbal-parallel buckle is used for a large retinal tear. Meridional folds of the pos the retina. Consider a horseshoe tear at terior edge of the tear are almost sure to 12 o'clock in the anterior equatorial zone form. E F F E C T OF INCREASED SURFACE AREA (Fig. 6, B). As the anteroposterior tension increases (as with a limbal-parallel buckle), OVER A BUCKLE—The effect of increased there is no opposing anterior tension to retinal surface area over a buckle is not posterior tension a t the posterior edge of clear. I t may explain the tendency of com the horseshoe tear, and no opposing pos pression folds on a long buckle to iron out terior force to anterior tension a t the in time. base of the flap, except perhaps from the SUMMARY vitreous, transmitted through the flap. The result is an anteroposterior elonga Tension analysis along the retinal sur tion of the tear, producing fishmouthing face demonstrates the advantage of meridi (Fig. 6, C). onal buckles over limbal-parallel buckles. A meridionally placed sponge will pro A cylindrical sponge generates tensional duce naso temporal tension, but less than forces in the retina along the long axis of half the anteroposterior tension produced the buckle and perpendicular to it. The by a limbal-parallel sponge. This smaller tension perpendicular to the sponge is nasotemporal tension from a meridional positive, and the retina and retinal pig sponge should distort the tear less (Fig. 6, ment epithelium stretch in that direction. D) ; in fact, we have never seen a fishmouth The tension along the long axis is positive laterally from a retinal break over a me (stretching) when the buckle is less than 90° arc length ; and negative (compression), ridional sponge. greater than 90° for a 5-mm sponge. Con EFFECT O F A LIMBAL-PARALLEL SPONGE GREATER THAN 90°—When a sponge whose sequently, retinal compression folds on the arc length is greater than 90° is placed, the buckles occur for buckles of arc length retina must fall on R P E which is shorter greater than 90°. These tension forces a t along the buckle's long axis than it was right angles to each other explain the de-
VOL. 79, NO. 6
RADIAL BUCKLING
velopment of (1) concave retinal detach ment or retinal folds off short limbal-parallel buckles, (2) retinal folds on long limbalparallel buckles, and (3) fishmouthing of horseshoe tears overlying a limbal-parallel buckle. The buckle increases retinal surface area overlying the buckle. The significance of this is not clear, but it may explain the lessening or disappearance of compression folds on the buckle in time.
965
New Orleans, for his advice in the derivation of the surface area of the buckle.
REFERENCES
1. Lincoff, H. A., and Kreissig, I.: The rationale for radial buckling. Am. J. Ophthalmol. 179: 955, 1975. 2. Meyer, H.: Meridional versus equatorial and latitudinal buckles in retinal detachment surgery. S. Afr. Med. J. 44 (Suppl.): 21, 1970. 3. Stallard, H. B.: Eyè Surgery, 4th ed. Bristol, John Wrigles and Sons Ltd., 1965, p. 699. 4. Hogan, M. J., Alvarado, J. A., and Weddell, ACKNOWLEDGMENTS J. E.: Histology of the Human Eye. Philadelphia, We thank Lyle Ferguson of T.A.N.O. Corporation, W. B. Saunders, 1971, pp. 187 and 328.
HERMAN M. BURIAN, M.D. 19061974 The dissemination of information about new books is a prime task of any periodical publication. This task can be fulfilled by appropriate publicity inserted by the publisher. More informative are—or should be—reviews of books by competent reviewers. Book reviews in ophthalmic publications are frequently disappointing. A review which simply lists the table of contents and concludes with à laudatory sentence tells the reader no more than the publisher's blurb or advertisement. The occasional humorous review of a serious book— making the author the straight man for some clown in the sticks, or the big city for that matter—is an injustice to the author and the readers. The usual polite reviews which quite obviously steer clear of any criti cal comment are of little use to the readers. On the reviewing of books Am. J. Ophthalmol. 66:756, 1968
