Helmholtz Schematic eye is used to deduce the theoretical formula. In this model the eye’s refractive system is considered a compound system consisting of two refractive systems: cornea (a single surface) and IOL (a thin lens with two surfaces). Refractive index (RI) of aqueous humor and vitreous fluid is 1.336. The intraocular lens is presumed to be a biconvex lens with equal curvature on both sides. The theoretical total eye refractive power is derived from the single surface power formula and compound lens calculation formula under the condition of SO tamponade or not.
Single surface power formula:
$$ \mathrm{D}\kern0.5em =\kern0.5em \frac{{\mathrm{n}}_1-{\mathrm{n}}_2}{\mathrm{r}} $$
D: refractive power of a single surface n1/n2: RI of substance at two sides of the single surface r: radius of refractive surface
Total refractive power of a thin lens:
$$ \mathrm{D}\kern0.5em =\kern0.5em {\mathrm{D}}_1\kern0.5em +\kern0.5em {\mathrm{D}}_2 $$
D: total refractive power D1/D2: refractive power of the lens’s two surfaces
Refractive power derivation of a compound or thick lens:
$$ \mathrm{D}\kern0.5em =\kern0.5em {\mathrm{D}}_1+{\mathrm{D}}_2-\frac{\mathrm{d}}{\mathrm{n}}{\mathrm{D}}_1{\mathrm{D}}_2 $$
D: total refractive power of a compound system D1/D2: refractive power of two single systems d: distance between two systems n: refractive index of substance between two systems
From the three formulas above, a theoretical formula of the total pseudophackic refractive power can be derived:
$$ {\mathrm{D}}_0\kern0.5em =\kern0.5em {\mathrm{D}}_{\mathrm{c}}+{\mathrm{D}}_{\mathrm{i}}\kern0.5em -\kern0.5em \frac{\mathrm{d}}{{\mathrm{n}}_{\mathrm{h}}}\ {\mathrm{D}}_{\mathrm{c}}{\mathrm{D}}_{\mathrm{i}}\kern0.5em =\kern0.5em {\mathrm{D}}_{\mathrm{c}}+\left(\frac{{\mathrm{n}}_{\mathrm{i}}-{\mathrm{n}}_{\mathrm{h}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{a}}}+\frac{{\mathrm{n}}_{\mathrm{i}}-{\mathrm{n}}_{\mathrm{v}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{p}}}\right)\kern0.5em -\kern0.5em \frac{\mathrm{d}}{{\mathrm{n}}_{\mathrm{h}}}\kern0.5em {\mathrm{D}}_{\mathrm{c}}\left(\frac{{\mathrm{n}}_{\mathrm{i}}-{\mathrm{n}}_{\mathrm{h}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{a}}}+\frac{{\mathrm{n}}_{\mathrm{i}}-{\mathrm{n}}_{\mathrm{v}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{p}}}\right) $$
D0: total refractive power of a pseudophakic eye Dc/D1: refractive power of cornea and IOL nv/ni/nh: RI of vitreous fluid, artificial lens and aqueous humor ria/rip: anterior and posterior radius of IOL d: distance from cornea to anterior surface of IOL (ACD)
When presumed unchanged corneal curvature and ACD after SO injection, a formula of theoretical refractive power with SO completely filled can be as follows:
$$ {\mathrm{D}}_1\kern0.5em =\kern0.5em {\mathrm{D}}_{\mathrm{c}}+\left(\frac{{\mathrm{n}}_{\mathrm{i}}-{\mathrm{n}}_{\mathrm{h}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{a}}}+\frac{{\mathrm{n}}_{\mathrm{i}}-{\mathrm{n}}_{\mathrm{so}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{p}}}\right)\kern0.5em -\kern0.5em \frac{\mathrm{d}}{{\mathrm{n}}_{\mathrm{h}}}\ {\mathrm{D}}_{\mathrm{c}}\left(\frac{{\mathrm{n}}_{\mathrm{i}}-{\mathrm{n}}_{\mathrm{h}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{a}}}+\frac{{\mathrm{n}}_{\mathrm{i}}-{\mathrm{n}}_{\mathrm{so}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{p}}}\right) $$
D1: total refractive power of a pseudophakic eye with SO completely filled nso: RI of silicone oil
From these two formulas we can derive the refractive shift formula from SO unfilled to completely filled:
If the IOL is presumed to be a biconvex lens with equal curvature on both sides, then a function of refractive power and RI of IOL can substitute for r
ip (from the single surface power formula):
$$ {\mathrm{r}}_{\mathrm{i}\mathrm{p}}\kern0.5em =\kern0.5em \frac{2\left({\mathrm{n}}_{\mathrm{i}}-{\mathrm{n}}_{\mathrm{h}}\right)}{{\mathrm{D}}_{\mathrm{i}}} $$
So the theoretical formula can be derived as:
When we substitute constants for some variables (n
v = 1.336, n
so = 1.403, n
h = 1.336), we obtain:
In this formula we can infer that refraction change of SO tamponade in pseudophakic eyes theoretically depends on IOL power, RI, ACD and corneal refractive power.
Clinical observations
Patients who underwent uneventful phacoemulsification, IOL implant, vitrectomy, SO tamponade and required SO extraction by one experienced surgeon were enrolled in this study, including highly myopic eyes. Exclusion criteria were unstable fundus (such as macular edema, macular pucker, retinal hemorrhage, or macular hole occurred after SO extraction), obviously SO emulsification obstructing optometry examinations, vitreous cavity incompletely filled, posterior capsule rupture, corneal opacity and incomplete clinical data. Silicone oil extraction was performed under inferior-temporal 23G pars plana incision and superior 20G incision. Both incisions were sutured after surgery. Refractive errors before and after SO extraction were confirmed by retinoscopy under dilated pupil and best spectacles correction. Corneal refractive power (Dc) was measured by corneal topography (ATLAS 9000,Carl Zeiss, Germany) before and after operation (postoperative Dc was used in theoretical calculation). Anterior chamber depth (ACD) was measured through ultrasonic A scan (E-Z Scan AB5500+, Sonomed, USA) after SO extraction, while preoperative ACD was not collected because of acoustic interference of some centrally accumulated emulsified silicone particles during supine examination. Axis length was detected pre/postoperatively by IOL master (Carl Zeiss, Germany). Six types of IOL were implanted in this patients group (Akreos adapt, Baush & Lomb, USA, RI 1.458; Akreos AO, Baush & Lomb, USA, RI 1.458; Softec HD, Lenstec, USA, RI 1.458; Tecnis ZCB00, AMO, USA, RI 1.470; Tecnis ZA9003, AMO, USA, RI 1.470; AR40e, AMO, USA, RI 1.470) and all patients were injected with 5000CS SO (RT SIL-OIL 5000, Carl Zeiss, Germany, RI 1.403). All the postoperative data were collected on the second day after surgery. Pearson linear correlation analysis was applied in correlation of refractive shift and selected variables. Paired T test was used to compare theoretical refractive shift with clinical result. All significant levels were designated as 0.05. All of those analyses were performed by an independent analyzer with software SAS 9.2. We declared that this study is in accordance with the declaration of Helsinki, approved by SIR RUN RUN SHAW hospital ethic committee and all patients have signed an informed consent, receiving no stipend.