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Shape Factor in the Penetration of Intraocular Foreign Bodies
Shape Factor in the Penetration of Intraocular Foreign Bodies Albert M. Potts, M.D., and John A. Distler, M.D.
We studied the way in which the shape of a missile striking the eye affects the ease of penetration of the central cornea. The test objects were enucleated pigs' eyes restored to normal intraocular pressure by cannulation of the optic nerve and connection of the cannula to a manometric system of physiologic saline. The shape, size, and weight of the missiles were carefully controlled. We attempted to keep these factors within the range of common civilian experience. Missile speed was measured photoelectrically. For each combination of weight and velocity, penetration of the missile was determined consistently, by the point shape. Penetration was most difficult for the blunt tip and least difficult for the knife-shaped tip. THE PRACTICING OPHTHALMOLOGIST in the United States is concerned primarily with intraocular foreign bodies that cause minimal disruption to the globe. Thanks to the information campaign of the National Society to Prevent Blindness, and the cooperation of both labor and management, this type of accident (usually industrial) has been reduced in incidence dramatically. Nevertheless, such events do occur and must be coped with. The report by Stewart! is noteworthy because of the care taken with controls. However, Stewart was concerned with military injuries and their prevention with protective lenses. Hence his missiles varied from 0.5 g to 215 g in weight, and his end point was "the ballistic limit"-the point at which the lens shattered, or the test eye (a fresh rabbit eye embed-
ded in gelatin) was penetrated so that the aqueous ran out. It has always been a source of wonder to us that a spherical BB fired from a few feet away rarely penetrates the globe, whereas a tiny chip from drill press or lathe with apparently much less driving force can become an intraocular foreign body. The quantitative studies with BBs that have already been published support this clinical impression. The shot used by Delori, Pomerantzeff, and Cox" averaged 345 mg in weight and if the velocity was kept below 62 m/sec, no penetration was observed in the pig eye imbedded in gelatin, which was the test object in their experiments. Tillett, Rose, and Herget! established that penetration by BBs occurred consistently at velocities above 72 m/sec. Thus, the no-penetration value represents a momentum of 24,840 mg-m/sec, a formidable figure indeed. The earlier reports by Weidenthal and Schepens! and by Cox, Schepens, and Freeman" dealt with contusion injuries in a less quantitative manner and have no direct bearing on the work described herein. It is the purpose of this article to report a series of experiments oriented to the civilian situation, using smaller particles, in which conditions were as carefully controlled as possible, and the major variable was the shape of the penetrating particle.
Material and Methods Our experimental arrangement is shown in Figure
1. The single-shot gun was a length of spinal needle
From the Departments of Ophthalmology of the University of Louisville, Louisville, Kentucky (Dr. Distler) and the University of Arizona, Tucson, Arizona (Dr. Potts). This research was supported by unrestricted grant funds of the Louise L. Sinton Foundation, Chicago, and Research to Prevent Blindness, New York. Reprint requests to Albert M. Potts, M.D., University of Arizona Health Sciences Center, 1501 N. Campbell Ave., Department of Ophthalmology, Tucson, AZ 85724.
tubing, properly. held in an aluminum alloy block and connected to a tank of nitrogen. In addition to the usual regulator valve on the tank, the outlet tubing to the gun was closed by a quick-release solenoid valve. A manometer between the release solenoid and the pressure regulator allowed us to measure the exact gas pressure driving each shot, and allowed exact duplication of conditions from experiment to experiment. The far end of the alloy block was drilled longitudi-
.©AMERICAN JOURNAL OF OPHTHALMOLOGY 100:183-187, JULY, 1985
183
184
July, 1985
AMERICAN JOURNAL OF OPHTHALMOLOGY
Oscilloscope
Alloy Block
*
Light Source
Fig. 1 (Potts and Distler). The experimental arrangement: air gun, speed-measurement device, and experimental eye.
nally to allow the missile to pass. At right angles to this passage and with axes exactly 90 degrees to the line traversed by the missile, three smaller holes were drilled with centers 1 em apart. On the near side of the missile path, each of the three openings carried a fiberoptic light pipe illuminated by a single light source. In each of the three openings opposite the light pipes were single photodiodes. The leads of the photodiodes were connected to the input of a dual-beam storage oscilloscope so that, as the missile passed the first opening, the pulse triggered the scope. Passing the second and third holes put a blip on each beam of the oscilloscope. Knowing the speed of the oscilloscope trace and the distance between holes allowed us to calculate the speed of the missile with accuracy. Missiles were made from the stylets of 18-,19-,20-, 22-, and 25-gauge spinal needles by cutting off an appropriate length and grinding each end to the appropriate shape on a carborundum stone. Each missile was weighed to the nearest tenth of a milligram. Six different point shapes were tested: flat (cylindrical), . 45-degree cone, 30-degree cone, 45degree chisel, 30-degree chisel, and knife edge (Fig. 2). The missile to be tested was muzzle loaded and the appropriate stylet was used to push it 6.5 ern into the barrel. The missile impinged axially on the cornea of the target pig eye. The eye had been cannulated through
the optic nerve and the cannula was connected to a water reservoir set at 27 cm of water pressure. A cardboard shield covering all sides of the target except the axis protected against ricochets and allowed retrieval of missiles that did not penetrate the eye. We fired each missile at ten to 15 different eyes. Each eye Was fired upon with ascending pressure (increasing velocity) until penetration was achieved or until the cornea was too damaged to give a reliable test. The cornea of the eye was changed slightly at each shot, so that a fresh surface would be presented each time. The endpoint for penetration was when the missile had completely passed the cornea and was in the anterior chamber. When a value shows gaussian distribution around a mean and the cumulative curve has a significant central portion that approaches a straight line, then the establishment of a lethal dose or an effective dose for 50% of the subjects has considerable significance. This is not true in our type of experiment. However, it is also true that each shot fired with what seems to be identical velocity does not penetrate the cornea. If it is recognized that the figure of merit for the velocity that causes penetration 50% of the time is not comparable with the pharmacologist's lethal dose for 50% of the test population, the 50% value may be used for what it is worth-a more useful statistic than 100% penetration, for e~mple.
Vol. 100, No. 1
185
Shape Factor in Foreign Bodies
<:l_
_ _I ~-----,I Blunt
1IIIIm
45° Cone
1
45° Chisel
__
30° Cone
30° Chisel Fig. 2 (Potts and Distler). Missile shapes.
Results Our results are presented in Figures 3 and 4. Our initial measurement on each missile is its velocity expressed as meters per second. However, since the striking force is measured better by momentum (milligram-meters per second), this is the measurement that should occupy our major attention. Even more rigorous would be the calculation of the kinetic energy of each particle, all of which is delivered to the cornea as the missile comes to a complete stop. Indeed, these changes in calculation make no difference in the outcome. The shape factors bear the same relation to each other in each series. Figure 3 depicts the results obtained with a single missile-the 22-gauge, 4S-degree chisel point-and is typical of the other sets of results. The velocity and the momentum required for penetration are not absolute, but neither are they symmetrical about a mean. The use of velocity and momentum needed for 50% penetration is as useful as any other single figure of merit, When these figures are plotted for momentum needed for 50% penetration vs diameter (Fig. 4), each shape produces a characteristic curve that is distinctive for that shape. No curve overlaps its neighbor- Special attention should be paid to the single point on this graph labeled "Knife Point" (see Figure 2 for the actual shape). It should be realized that the single point on the graph represents a series of trials, as shown in Figure 3, although they are performed with a single-gauge missile only. Its validity is as great as that of any of the other single
~~---I
Knife
points that make up the curves in the graph. Each individual point gives important data on the shape factor. A few human eyes unsuitable for use as keratoplasty donors were made available to us for this series of experiments before they were fixed for routine study. It was found that, although pig corneas were almost twice as thick as the human specimens, the ease (or difficulty) of penetration by an IS-gauge blunt missile was almost identical for the two types of eye. This suggests that the tensile strength of the human collagen-mucopolysaccharide network is significantly higher than that of the pig.
Discussion It seems to us that our experiments have operationally defined the condition for penetration of the cornea by foreign bodies that possess energy in the range that will allow penetration without destroying the globe. The existence of the curves in Figure 4 is ample evidence that equations can be written to describe the experimental conditions. However, it is clear that corneal resistance will have to be defined by an empirical constant. Once one departs from the regular geometric shapes used by us, the shape factor will be very difficult indeed to define. Rather than try to establish immutable rules about the penetration of foreign bodies, it seems more important to understand the experimental data on a
Vso =48.21
Partial Penetration
Complete Penetration
30
40
50
55
Fig. 3 (Potts and Distler). Results with 22-gauge, 45-degree chisel point. Vse indicates the velocity necessary for penetration of 50% of the eyes; Moo the momentum necessary for penetration of 50% of the eyes.
Velocity: Meters/Second
M S O=3 0 .3 7
Partial Penetration
Complete Penetration
25
20
30
35
Momentum: Milligram - Meters/Second
90 80 o
70
"E
60
QI 11l
Blunt 18
19
Gauge
20
22
45° Cone 45° Chisel 300 Cone 3cf Chisel
Fig. 4 (Potts and Distler). Characteristic curves for each shape of missile.
Cl
-E
50
c:
40
E
:J
QI
E
0 ~
30 20 10
25
Knife Point
@ .80 .70 .60 .50 .40 Diameter (rnrn)
Vol. 100, No. 1
187
Shape Factor in Foreign Bodies
logical basis. Two fundamental concepts are required. The first is the structure of the cornea as layers of parallel collagen fibrils bound together by mucopolysaccharide, with each succeeding layer of fibrils at right angles to the one above and below. 6 The second fundamental concept concerns the physics of cutting, about which little is available in the literature. The apocryphal story of a 1l0-lb flight attendant on spike heels perforating the aluminum decking in the aisle of a commercial airplane is illustrative. If the spike heel had an area of only one-fifth of 1 inch", the flight attendant was delivering 550 lbs/inch" at each step. This is clearly the principle of operation of a sharp surgical knife. The several ounces of wrist pressure are delivered to the tissue by a blade whose width is 1 um or less at the point of contact. Remember that in microtomy for the electron microscope, a "thick" section is 1 f.Lm thick. Thus, the multiplication factor for applied force at the contact point of a scalpel blade is many thousand times that of the hand guiding it. When one is working at the submicrometer level, other considerations enter the picture. Application of so much force in such a restricted space must generate a significant amount of heat that cannot be dissipated instantaneously in tissue. One result is protein denaturation at the site of cutting, which may well aid the cutting process. Generated heat may also playa role in the eventual dulling of the blade after continuous use. This, however, is of only passing interest; let us return to the penetration of intraocular foreign bodies. Each of the missiles that we have used to obtain experimental data sets itself the same problem. On impact it must create a circular hole equal in diameter to the diameter of the cylinder and still have enough force left to penetrate into the anterior chamber. Some of the results obtained agree with intuitive reasoning. It was not surprising to find that the flat-ended cylinders required the most energy to penetrate, and that the larger the diameter, the more the required energy. Such missiles had to burst each of the successive layers of mucopolysaccharidebound collagen. The greater the diameter, the greater the area of corneal microstructure that had to be burst. In the case of the cone-tipped missiles, one can visualize the first few micrometers of stroma being penetrated rapidly by the "spike-heel effect." As penetration continues, this multiplier of force diminishes sharply as the penetrating portion of the missile reaches the full diameter of the cylinder. As the point becomes "sharper" (30-degree cone compared with a 45-degree cone) the effect is prolonged because the tapered portion is longer. Additionally, it seems probable that in the cone-tipped projectile part of the energy is expended in pushing stromal substance aside. As the taper increases, the force
vector normal to the surface of the cone (which accomplishes this pushing) increases in magnitude. Intuitively, one would have said that the chiseltipped missile would have penetrated the cornea more easily than the cone-tipped one in all instances, because the chisel edge would be expected to continue to cut collagen fibers through the entire corneal thickness with the mechanical advantage conferred by its thin edge. This proves not to be the case. For any given missile diameter, the 45-degree chisel tip penetrated with more ease than the 45-degree cone, but with less ease than the 30-degree cone. However, the 30-degree chisel-tipped missile penetrated with still greater ease. Apparently, the fact that in the chisel-tipped missile the sharpened edge is the full original diameter plays a significant role. This allows the 30-degree cone, sharpened through 360 degrees, to penetrate with greater ease than the 45-degree chisel. This reasoning led us to fabricate the knife-edged missile shown in Figure 2. Although we used only one size (20-gauge), and the results in Figure 4 are expressed as a single point, the validity of that point was established by just as many trials as the other points on the graph. The knife-edge category is in a class by itself in its ease of penetration. In this missile alone, the mechanical advantage of the cutting edge is exerted until the hole it makes is the full diameter of the cylindrical portion of the missile. For the 20-gauge missile, 17 mg-m/sec is all the momentum required for penetration. Compare this to the no-penetration value of 24,840 mg-m/sec found by Delori, Pomerantzeff, and Cox" for the BB. It seems that our clinical impression is justified by experimental fact. It is the knife-edged particles produced by industrial processes that so easily penetrate the globe.
References 1. Stewart, G. M.: Eye protection against small highspeed missiles. Am. J. Ophthalmol. 51:80, 1961. 2. Delori, F., Pomerantzeff, 0., and Cox, M.S.: Deformation of the globe under high speed impact. Its relation to contusion injuries. Invest. Ophthalmol. 8:290, 1969. 3. Tillett, C. W., Rose, H. W., and Herget, c.. Highspeed photographic study of perforating ocular injury by the BB. Am. J. Ophthalmol. 54:675, 1962. 4. Weidenthal, D. T., and Schepens, C. 1.: Peripheral fundus changes associated with ocular contusion. Am. J. Ophtha!mol. 62:465, 1966. 5. Cox, M.S., Schepens, C. 1., and Freeman, H. M.: Retina! detachment due to ocular contusion. Arch. Ophtha!mol. 76:678, 1966. 6. Iakus, M. A.: Studies on the cornea: I. The fine structure of the rat cornea. Am. J. Ophtha!mol. 38(suppl.):40, 1954.
We studied the way in which the shape of a missile striking the eye affects the ease of penetration of the central cornea. The test objects were enucleated pigs' eyes restored to normal intraocular pressure by cannulation of the optic nerve and connection of the cannula to a manometric system of physiologic saline. The shape, size, and weight of the missiles were carefully controlled. We attempted to keep these factors within the range of common civilian experience. Missile speed was measured photoelectrically. For each combination of weight and velocity, penetration of the missile was determined consistently, by the point shape. Penetration was most difficult for the blunt tip and least difficult for the knife-shaped tip. THE PRACTICING OPHTHALMOLOGIST in the United States is concerned primarily with intraocular foreign bodies that cause minimal disruption to the globe. Thanks to the information campaign of the National Society to Prevent Blindness, and the cooperation of both labor and management, this type of accident (usually industrial) has been reduced in incidence dramatically. Nevertheless, such events do occur and must be coped with. The report by Stewart! is noteworthy because of the care taken with controls. However, Stewart was concerned with military injuries and their prevention with protective lenses. Hence his missiles varied from 0.5 g to 215 g in weight, and his end point was "the ballistic limit"-the point at which the lens shattered, or the test eye (a fresh rabbit eye embed-
ded in gelatin) was penetrated so that the aqueous ran out. It has always been a source of wonder to us that a spherical BB fired from a few feet away rarely penetrates the globe, whereas a tiny chip from drill press or lathe with apparently much less driving force can become an intraocular foreign body. The quantitative studies with BBs that have already been published support this clinical impression. The shot used by Delori, Pomerantzeff, and Cox" averaged 345 mg in weight and if the velocity was kept below 62 m/sec, no penetration was observed in the pig eye imbedded in gelatin, which was the test object in their experiments. Tillett, Rose, and Herget! established that penetration by BBs occurred consistently at velocities above 72 m/sec. Thus, the no-penetration value represents a momentum of 24,840 mg-m/sec, a formidable figure indeed. The earlier reports by Weidenthal and Schepens! and by Cox, Schepens, and Freeman" dealt with contusion injuries in a less quantitative manner and have no direct bearing on the work described herein. It is the purpose of this article to report a series of experiments oriented to the civilian situation, using smaller particles, in which conditions were as carefully controlled as possible, and the major variable was the shape of the penetrating particle.
Material and Methods Our experimental arrangement is shown in Figure
1. The single-shot gun was a length of spinal needle
From the Departments of Ophthalmology of the University of Louisville, Louisville, Kentucky (Dr. Distler) and the University of Arizona, Tucson, Arizona (Dr. Potts). This research was supported by unrestricted grant funds of the Louise L. Sinton Foundation, Chicago, and Research to Prevent Blindness, New York. Reprint requests to Albert M. Potts, M.D., University of Arizona Health Sciences Center, 1501 N. Campbell Ave., Department of Ophthalmology, Tucson, AZ 85724.
tubing, properly. held in an aluminum alloy block and connected to a tank of nitrogen. In addition to the usual regulator valve on the tank, the outlet tubing to the gun was closed by a quick-release solenoid valve. A manometer between the release solenoid and the pressure regulator allowed us to measure the exact gas pressure driving each shot, and allowed exact duplication of conditions from experiment to experiment. The far end of the alloy block was drilled longitudi-
.©AMERICAN JOURNAL OF OPHTHALMOLOGY 100:183-187, JULY, 1985
183
184
July, 1985
AMERICAN JOURNAL OF OPHTHALMOLOGY
Oscilloscope
Alloy Block
*
Light Source
Fig. 1 (Potts and Distler). The experimental arrangement: air gun, speed-measurement device, and experimental eye.
nally to allow the missile to pass. At right angles to this passage and with axes exactly 90 degrees to the line traversed by the missile, three smaller holes were drilled with centers 1 em apart. On the near side of the missile path, each of the three openings carried a fiberoptic light pipe illuminated by a single light source. In each of the three openings opposite the light pipes were single photodiodes. The leads of the photodiodes were connected to the input of a dual-beam storage oscilloscope so that, as the missile passed the first opening, the pulse triggered the scope. Passing the second and third holes put a blip on each beam of the oscilloscope. Knowing the speed of the oscilloscope trace and the distance between holes allowed us to calculate the speed of the missile with accuracy. Missiles were made from the stylets of 18-,19-,20-, 22-, and 25-gauge spinal needles by cutting off an appropriate length and grinding each end to the appropriate shape on a carborundum stone. Each missile was weighed to the nearest tenth of a milligram. Six different point shapes were tested: flat (cylindrical), . 45-degree cone, 30-degree cone, 45degree chisel, 30-degree chisel, and knife edge (Fig. 2). The missile to be tested was muzzle loaded and the appropriate stylet was used to push it 6.5 ern into the barrel. The missile impinged axially on the cornea of the target pig eye. The eye had been cannulated through
the optic nerve and the cannula was connected to a water reservoir set at 27 cm of water pressure. A cardboard shield covering all sides of the target except the axis protected against ricochets and allowed retrieval of missiles that did not penetrate the eye. We fired each missile at ten to 15 different eyes. Each eye Was fired upon with ascending pressure (increasing velocity) until penetration was achieved or until the cornea was too damaged to give a reliable test. The cornea of the eye was changed slightly at each shot, so that a fresh surface would be presented each time. The endpoint for penetration was when the missile had completely passed the cornea and was in the anterior chamber. When a value shows gaussian distribution around a mean and the cumulative curve has a significant central portion that approaches a straight line, then the establishment of a lethal dose or an effective dose for 50% of the subjects has considerable significance. This is not true in our type of experiment. However, it is also true that each shot fired with what seems to be identical velocity does not penetrate the cornea. If it is recognized that the figure of merit for the velocity that causes penetration 50% of the time is not comparable with the pharmacologist's lethal dose for 50% of the test population, the 50% value may be used for what it is worth-a more useful statistic than 100% penetration, for e~mple.
Vol. 100, No. 1
185
Shape Factor in Foreign Bodies
<:l_
_ _I ~-----,I Blunt
1IIIIm
45° Cone
1
45° Chisel
__
30° Cone
30° Chisel Fig. 2 (Potts and Distler). Missile shapes.
Results Our results are presented in Figures 3 and 4. Our initial measurement on each missile is its velocity expressed as meters per second. However, since the striking force is measured better by momentum (milligram-meters per second), this is the measurement that should occupy our major attention. Even more rigorous would be the calculation of the kinetic energy of each particle, all of which is delivered to the cornea as the missile comes to a complete stop. Indeed, these changes in calculation make no difference in the outcome. The shape factors bear the same relation to each other in each series. Figure 3 depicts the results obtained with a single missile-the 22-gauge, 4S-degree chisel point-and is typical of the other sets of results. The velocity and the momentum required for penetration are not absolute, but neither are they symmetrical about a mean. The use of velocity and momentum needed for 50% penetration is as useful as any other single figure of merit, When these figures are plotted for momentum needed for 50% penetration vs diameter (Fig. 4), each shape produces a characteristic curve that is distinctive for that shape. No curve overlaps its neighbor- Special attention should be paid to the single point on this graph labeled "Knife Point" (see Figure 2 for the actual shape). It should be realized that the single point on the graph represents a series of trials, as shown in Figure 3, although they are performed with a single-gauge missile only. Its validity is as great as that of any of the other single
~~---I
Knife
points that make up the curves in the graph. Each individual point gives important data on the shape factor. A few human eyes unsuitable for use as keratoplasty donors were made available to us for this series of experiments before they were fixed for routine study. It was found that, although pig corneas were almost twice as thick as the human specimens, the ease (or difficulty) of penetration by an IS-gauge blunt missile was almost identical for the two types of eye. This suggests that the tensile strength of the human collagen-mucopolysaccharide network is significantly higher than that of the pig.
Discussion It seems to us that our experiments have operationally defined the condition for penetration of the cornea by foreign bodies that possess energy in the range that will allow penetration without destroying the globe. The existence of the curves in Figure 4 is ample evidence that equations can be written to describe the experimental conditions. However, it is clear that corneal resistance will have to be defined by an empirical constant. Once one departs from the regular geometric shapes used by us, the shape factor will be very difficult indeed to define. Rather than try to establish immutable rules about the penetration of foreign bodies, it seems more important to understand the experimental data on a
Vso =48.21
Partial Penetration
Complete Penetration
30
40
50
55
Fig. 3 (Potts and Distler). Results with 22-gauge, 45-degree chisel point. Vse indicates the velocity necessary for penetration of 50% of the eyes; Moo the momentum necessary for penetration of 50% of the eyes.
Velocity: Meters/Second
M S O=3 0 .3 7
Partial Penetration
Complete Penetration
25
20
30
35
Momentum: Milligram - Meters/Second
90 80 o
70
"E
60
QI 11l
Blunt 18
19
Gauge
20
22
45° Cone 45° Chisel 300 Cone 3cf Chisel
Fig. 4 (Potts and Distler). Characteristic curves for each shape of missile.
Cl
-E
50
c:
40
E
:J
QI
E
0 ~
30 20 10
25
Knife Point
@ .80 .70 .60 .50 .40 Diameter (rnrn)
Vol. 100, No. 1
187
Shape Factor in Foreign Bodies
logical basis. Two fundamental concepts are required. The first is the structure of the cornea as layers of parallel collagen fibrils bound together by mucopolysaccharide, with each succeeding layer of fibrils at right angles to the one above and below. 6 The second fundamental concept concerns the physics of cutting, about which little is available in the literature. The apocryphal story of a 1l0-lb flight attendant on spike heels perforating the aluminum decking in the aisle of a commercial airplane is illustrative. If the spike heel had an area of only one-fifth of 1 inch", the flight attendant was delivering 550 lbs/inch" at each step. This is clearly the principle of operation of a sharp surgical knife. The several ounces of wrist pressure are delivered to the tissue by a blade whose width is 1 um or less at the point of contact. Remember that in microtomy for the electron microscope, a "thick" section is 1 f.Lm thick. Thus, the multiplication factor for applied force at the contact point of a scalpel blade is many thousand times that of the hand guiding it. When one is working at the submicrometer level, other considerations enter the picture. Application of so much force in such a restricted space must generate a significant amount of heat that cannot be dissipated instantaneously in tissue. One result is protein denaturation at the site of cutting, which may well aid the cutting process. Generated heat may also playa role in the eventual dulling of the blade after continuous use. This, however, is of only passing interest; let us return to the penetration of intraocular foreign bodies. Each of the missiles that we have used to obtain experimental data sets itself the same problem. On impact it must create a circular hole equal in diameter to the diameter of the cylinder and still have enough force left to penetrate into the anterior chamber. Some of the results obtained agree with intuitive reasoning. It was not surprising to find that the flat-ended cylinders required the most energy to penetrate, and that the larger the diameter, the more the required energy. Such missiles had to burst each of the successive layers of mucopolysaccharidebound collagen. The greater the diameter, the greater the area of corneal microstructure that had to be burst. In the case of the cone-tipped missiles, one can visualize the first few micrometers of stroma being penetrated rapidly by the "spike-heel effect." As penetration continues, this multiplier of force diminishes sharply as the penetrating portion of the missile reaches the full diameter of the cylinder. As the point becomes "sharper" (30-degree cone compared with a 45-degree cone) the effect is prolonged because the tapered portion is longer. Additionally, it seems probable that in the cone-tipped projectile part of the energy is expended in pushing stromal substance aside. As the taper increases, the force
vector normal to the surface of the cone (which accomplishes this pushing) increases in magnitude. Intuitively, one would have said that the chiseltipped missile would have penetrated the cornea more easily than the cone-tipped one in all instances, because the chisel edge would be expected to continue to cut collagen fibers through the entire corneal thickness with the mechanical advantage conferred by its thin edge. This proves not to be the case. For any given missile diameter, the 45-degree chisel tip penetrated with more ease than the 45-degree cone, but with less ease than the 30-degree cone. However, the 30-degree chisel-tipped missile penetrated with still greater ease. Apparently, the fact that in the chisel-tipped missile the sharpened edge is the full original diameter plays a significant role. This allows the 30-degree cone, sharpened through 360 degrees, to penetrate with greater ease than the 45-degree chisel. This reasoning led us to fabricate the knife-edged missile shown in Figure 2. Although we used only one size (20-gauge), and the results in Figure 4 are expressed as a single point, the validity of that point was established by just as many trials as the other points on the graph. The knife-edge category is in a class by itself in its ease of penetration. In this missile alone, the mechanical advantage of the cutting edge is exerted until the hole it makes is the full diameter of the cylindrical portion of the missile. For the 20-gauge missile, 17 mg-m/sec is all the momentum required for penetration. Compare this to the no-penetration value of 24,840 mg-m/sec found by Delori, Pomerantzeff, and Cox" for the BB. It seems that our clinical impression is justified by experimental fact. It is the knife-edged particles produced by industrial processes that so easily penetrate the globe.
References 1. Stewart, G. M.: Eye protection against small highspeed missiles. Am. J. Ophthalmol. 51:80, 1961. 2. Delori, F., Pomerantzeff, 0., and Cox, M.S.: Deformation of the globe under high speed impact. Its relation to contusion injuries. Invest. Ophthalmol. 8:290, 1969. 3. Tillett, C. W., Rose, H. W., and Herget, c.. Highspeed photographic study of perforating ocular injury by the BB. Am. J. Ophthalmol. 54:675, 1962. 4. Weidenthal, D. T., and Schepens, C. 1.: Peripheral fundus changes associated with ocular contusion. Am. J. Ophtha!mol. 62:465, 1966. 5. Cox, M.S., Schepens, C. 1., and Freeman, H. M.: Retina! detachment due to ocular contusion. Arch. Ophtha!mol. 76:678, 1966. 6. Iakus, M. A.: Studies on the cornea: I. The fine structure of the rat cornea. Am. J. Ophtha!mol. 38(suppl.):40, 1954.