{"responseHeader":{"status":0,"QTime":3,"params":{"q":"{!q.op=AND}id:\"705805\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"volume_t":"16","date_modified_t":"2008-03-26","ark_t":"ark:/87278/s64464zm","date_digital_t":"2007-11-13","setname_s":"ir_uspace","subject_t":"Keratoplasty; Trabecular Collapse; Angle Disrottion; Elevated Pressure; Aphakia; Mathematics","restricted_i":0,"department_t":"Ophthalmology","format_medium_t":"application/pdf","creator_t":"Olson, Randall J.","identifier_t":"ir-main,2069","unid_t":"33763","date_t":"1977-12","bibliographic_citation_t":"Olson RJ; Kaufman HE. A mathematical description of causative factors and prevention of elevated intraocular pressure after keratoplasty. Invest Ophthalmol Vis Sci. 1977 Dec;16(12):1085-92. Retrieved on November 13, 2007 from http://www.ncbi.nlm.nih.gov/sites/entrez","mass_i":1515011812,"publisher_t":"Association for Research in Vision and Ophthalmology","description_t":"In keratoplasty with grafts the same size as the recipient bed, tight sutures and thick recipient corneal periphery distort the angle and may collapse the filtering meshwork. This can cause very high postoperative pressures, which can be avoided by the use of donor grafts larger than the recipient bed. These relationships can be mathematically predicted.","first_page_t":"1085","rights_management_t":"(c) Association for Research in Vision and Ophthalmology","title_t":"Mathematical description of causative factors and prevention of elevated intraocular pressure after keratoplasty","id":705805,"publication_type_t":"Journal Article","parent_i":0,"type_t":"Text","thumb_s":"/6a/5d/6a5db46cbae941390a5decb7f2bed033c1afbacb.jpg","last_page_t":"1092","oldid_t":"uspace 3651","metadata_cataloger_t":"CMS","format_t":"application/pdf","subject_mesh_t":"Mathematics; Postoperative Complications; Corneal Transplantation; Suture Techniques","modified_tdt":"2012-06-13T00:00:00Z","school_or_college_t":"School of Medicine","language_t":"eng","issue_t":"12","file_s":"/e5/47/e54729dae4e232e730b4f308a89b0d88feb48ef0.pdf","other_author_t":"Kaufman, Herbert E.","created_tdt":"2012-06-13T00:00:00Z","_version_":1679953028633853952,"ocr_t":"Articles A mathematical description of causative factors and prevention of elevated intraocular pressure after keratoplasty Randall J. Olsono and Herbert E. Kaufman In keratoplasty with grafts the same size as the recipient bed, tight sutures and thick recipient corneal periphery distort the angle and may collapse the filtering meshwork. This can cause very high postoperative pressures, which can be avoided by the use of donor grafts larger than the recipient bed. These relationships can be mathematically predicted. Key words: keratoplasty, trabecular collapse, angle distortion, elevated pressure, aphakia. ~th the advent of electronic applanation tonometry and its proved efficacy in the face of edematous or irregular corneas, I-3 it was discovered that most patients undergoing aphakic keratoplasty and even more in keratoplasty with cataract extraction would have elevated pressures postoperatively. Irvine and Kaufman4 had a mean maximum pressure rise of 40 mm. Hg in aphakic transplants and of 50 mm. Hg in combined transplants and cataract extraction. This was not related to preoperative glaucoma, and on gonioscopy, angle From the Department of Ophthalmology, University of Florida College of Medicine, Gainesville. Supported in part by grants EY 00446 and EY 00266 from the National Eye Institute and a °Bausch & Lomb Fellowship. Submitted for publication Aug. 15, 1977. Reprint requests: Department of Ophthalmology, L.S.U. Medical Center, 136 South Roman St., New Orleans, La. 70112. 1085 closure was not seen. Phakic grafts, on the other hand, did not have a postoperative pressure problem. .., Wood et aJ.5 further showed that· this pressure rise would usually return to normal levels over a period of days to a few weeks and found little change in the pressure with acetazolamide treatment. Although this is usually the case, it has been our experience that a significant percentage of patients go on to have severe pressure problems that can be resistant to all modes of medical treatment and eventually require cyclocryotherapy. Zimmerman et al.6 have shown that in phakic transplants done in eyebank eyes, there is no outflow facility change with kera~ toplasty. Such was not the case with aphakic keratoplasty in eyebank eyes, where perfusion studies showed an average of 37 percent decrease in outflow facility compared to the control after keratoplasty where the donor and recipient trephines were the same 1086 Olson and Kaufman Fig. 1. Angle relationships before (al and at') and after (a~ and a2') . suturing in keratoplasty. size. Further work with an 8.0 mm. donor in a 7.5 mm. bed blocked this decrease in outHow.7 At the University of Florida and Washington University, St. Louis, a randomized study9 has just been completed that clearly showed a decreased postoperative intraocular pressure in aphakic and combined- procedure keratoplasties where a donor 0.5 mm. larger than the recipient bed was used. This improvement was not so great when an 8.5 mm. donor in an 8.0 mm. recipient was used as compared to an 8.0 mm. donor in a 7.5 mm. recipient. This paper is a mathematical presentation of factors altering the angIe after keratoplasty in an attempt to explain what is happening in postkeratoplasty elevated intraocular pressure. Mathematical derivation Keratoplasty in cross-section leaves two recipient corneal arms with a certain thickness (Ct ) and length from the limbus (01). For the purpose of this paper we will consider a keratoplasty that is perfectly centered. The central wound (WI) has a diameter equal to the trephine diameter. The corneal diameter limbus to limbus ( Ll) is also a measurable item. After suturing of the donor cornea all these relationships can change by the effect of tissue compression and shortening by the suture as well as a possibly larger or smaller donor cornea compared to the original wound size (WI). We will call these postsuturing relationships 02, W2, and L2, and all of these can be measured. Invest. Ophthalmol. Visual Sci. December 1977 The peripheral cornea has a certain radius of curvature (Rl ), and suturing could change this by pulling and flattening the recipient cornea ( R2)' The only other definitions we need to begin our derivation is the definition of five angles (Fig. 1) . al we will define as the angle from the limbal plane to the chord of the recipient cornea before suturing. a2 is the same angle after suturing. at' is the angle between the chord of the recipient cornea and the tangent to the cornea at the limbus, whereas a/ is the same relationship to a2 after suturing. We will start out by trying to explain the change in the angle of the tangent to the cornea at the limbus from a fresh and untouched eye, to that same angle after keratoplasty and call this change a. a = al + aI' - a2 - a/ We have defined alpha in terms of four angles, and now we will see if we can define each of the angles in terms of Ll, L~, WI, W2, 0 1, 02, Rl, and R2 (Fig. 2). and \" .\\ The deri~ation of at' + a2' is a little more difficult. The angle between the radius and the perpendicular dropped from the chord 0 1 to the center of the corneal curve is equal to at' because its opposing acute angle and at' make up a right angle (the tangent is always perpendicular -i.e., 90 degrees to the radius of a circle at its point of contact) (Fig. 3). Our perpendicular to the chord through the center of curvature bisects the chord because the chord plus two radii through the point of intersection of the chord and the circle make up an isosceles triangle. Now we can define at' in tenns of things we know. . , Vz chord length _ Vz Dl SIn a l = --- Rl Rl I t then follows that: Sin a/ It is also apparent that a cross-section of the limbal plane is a chord that intersects the cornea at the point of contact of the limbal tangent to the cornea. From our foregoing analYSis, then, the angle between the limbal chord and the linlbal tangent which we called al + at' is equal to the angle whose sine is half the chord length over the radius. Therefore: Volume 16 Number 12 Mathematics of elevated lOP after keratoplasty 1087 Fig. 2. Cornea in cross-section. Fig. 3. Cornea in cross-section. R1, Peripheral corneal radius of curvature. This statement is only truly accurate for a perfectly regular corneal radius which the cornea is not, but in the discussion and the use of experimental data this will be an easy way to check for gross errors in technique. One assumption made is that the peripheral cornea is part of a true circle. This should be a fairly accurate assumption, since 0 1 and 02 are small lengths in reference to Rl and R2 and also that at' + a/ are small angles and will tend to cancel each other out. Our angle a or the change seen at the angle caused by suturing is: ( Ll - WI) + Sin-1 (~) 201 2Rl - Cos-1 (L2 2~ Wi) - Sin-t (~~) This change in angle a will have a real effect on the trabecular area because the cornea is not a thin line but has a definite thickness (Ct). We have calculated what happens externally only. Internally the story is different, and it is internally that the trabecular meshwork is. The anterior surface will act as a fixed surface because our measurements will be taken there. The interior surface will necessarily be compressed, and this compression will have some relationship to our angle a. We will treat a thin slice of peripheral cornea fixed at the limbus as a rectangle that after suturing rotates through an angle already defined as a (Fig. 4). The triangle so formed is a good approximation of the amount of tissue compressed. The internal dimension of this triangle we will call B. B Tan a == Ct 1088 Olson and Kaufman Invest. Ophthalmol. Visual Sci. December 1977 PERIPHERAL CORNEA PRIOR TO SUTURING PERIPHERAL CORNEA AFTER SUTURING Fig. 4. Corneal cross-section showing the tissue compressed in the angle with keratoplasty. Wound Compression in mm (equal on donor a recipient side) Fig. 5. Relationship of wound compression and angle a (12.00 mm. corneal diameter). so that B = Tan a Ct The area of this triangle would be: B x Ct 2 How trabecular resistance (R) is related to the dimension of B or the area of the compressed triangle is unclear. Definitive evidence of such a relationship does not exist, but an angle change is probably occurring. We will look at B as having a linear relationship with R and also as having an exponential rel'ationship, which is much more likely. An exponential relationship would say that for the first increment of compression internally we would not expect much change in R but that later as critical levels of compression and distortion occur, there would be a greater incremental increase in resistance for each increment of tissue distortion. Plotting resistance as the Y axis and internal tissue change ( B) as the X axis we have 1. Linear relationship: R = AL + E = A Ct Tan a + E 2. Exponential relationship: In R = A Ct Tan a+E The Y intercept will have to be the initial resistance (Ro ) because no change in the corneal curve will not cause a change in resistance. Constant A, or the slope of our relationship between tissue compression and resistance, is not known at the present time. Now we can look at changes in intraocular Volume 16 Number 12 Mathematics of elevated lOP after keratoplasty 1089 ,7 ee 8c~: e:1.-c5 o \"0 e ,6 cO ~N E E ,z=....; e 'E c. e ';: 0 Ql Ql '5. Cl. >- oj 'u ~ 't;; (; Q: c 0. ,5 c 0 0 0 ~ ~ ,z= .j .4 ~ 0. c: c c ,3 E ~ .~ .!: Ql .2 ~ ~ ~ .u. .1 UJ o Wound Compression in mm (equal on donor a recipient side) Fig. 6. Relationship of wound compression and internal angle relaxation (12.0 mm. corneal diameter). pressure as related to angle a in this experimental model. l. For a linear relationship: Po = FACt Tan a + Pv 2. For an exponential , relationship: P .. = FeACt Ton a Ro + Pv Where Po is intraocular pressure, Pv is scleral venous pressure, and F is aqueous How. It should be noted that resistance and intraocular pressure could be related to the area of the compressed triangle. This would change the two equations by simply squaring Ct. Discussion This model accurately predicts which factors will increase the angle distortion and which factors might reduce it. Tight suturing and long bits with more compressed tissue, larger trephine sizes, smaller total recipient corneal diameter, and increased peripheral corneal thickness' will aggravate the problem. Less tight wounds, smaller trephines, donor corneas larger than the recipient, thinner corneas, and larger over-all corneal diameter, by the same token, will all tend to alleviate this problem. The relationship is also interesting in that it is not linear for any of the alleviating factors mentioned except poSSibly corneal thickness. The ramifications of that statement are great, let us consider a few of them. With the angle plotted as a function of wound compression (Fig. 5), we see a gentle slope becoming quite steep, but the steep range depends on all the other factors mentioned. We have plotted several donor recipient combinations and see that the worst combination is the 8.0 mm. recipient with the same donor size. The 6.0 mm. trephine has a curve that needs greater compression for the same change in angle lX, with the 8.5 mm. donor with the 8.0 mm. recipient even better. When internal angle compression is considered, the same picture occurs but is even more accentuated. Fig. 6 shows this for several combinations of donor-recipient size with one example of a peIipheral cor- 1090 Olson and Kaufman Invest. Ophthalmol. Visual Sci. December 1977 e e e e 10 e q ,..: .6 e IX) E 'E CII ! '5, 'u ~ .5 e CII 1/1 eO:: Q00 . 1