Peter R. Greene

Time course of rhesus lid-suture myopia

Axial-length and refraction measurements are presented for the lid-sutured rhesus monkey at 6-month intervals during the first 1.5 years of life. The experimental data are fitted to an exponential growth theory allowing the calculation of time constants, apparent time origins, and correlation coefficients for 10 eyes from five animals. On average, axial length develops with a time constant of 0.40 year for lid-suture myopia, compared with 0.42 year for the normal eye. A practical application of this work is that one must allow 1.6 years of lid suture to achieve 95% of the total refractive or axial-length change.

Optical constants and dimensions for the myopic, hyperopic and normal rhesus eye

Complete optical constants and physical dimensions are presented for eight ametropic rhesus eyes in the range from -11.00 diopters of myopia to +8.00 diopters of hyperopia and compared with the same measurements from 40 essentially emmetropic normal control eyes. The optical constants are calculated from a Gullstrand analysis modified for the rhesus eye, and include focal lengths, cardinal points, lens power and total optical power. The physical dimensions, from keratometry and ultrasound, include corneal radius, anterior chamber depth, lens thickness, vitreous depth and axial length. A regression analysis of the data shows that refraction is strongly correlated with both axial length and vitreous depth (at the rate of 3.7 and 4.2 diopters mm-1, respectively; correlation coefficients of -0.962 and -0.821) but is essentially independent of lens power, corneal power, and total optical power. These results allow us to infer that experimentally induced ametropia in the rhesus is caused by a distortion of the globe, and is not caused by the cornea or the lens.

Optimal geometry for oval sprint tracks

Track aspect ratio is defined as the percentage of lap length devoted to turns on an oval running track. Equations based on experiments are developed to model a composite runner with a specified top speed, during an acceleration phase in the straightaways and a centripetal phase in the turns. We calculate velocity deficits for several common track sizes over the range of aspect ratios and predict that, under our assumptions, a perfect circle is the optimal track shape.

Emmetropia Approach Dynamics with Diurnal Dual-phase Cycling

Numerical experiments are performed on a first order exponential response function subjected to a diurnal square wave visual environment with variable duty cycle. The model is directly applicable to exponential drift of focal status. A two-state square wave is employed as the forcing function with high B for time H and low A for time L. Duty cycles of (1/3), (1/2) and (2/3) are calculated in detail. Results show the following standard linear system response: (1) Unless the system runs into the stops, the ready state equilibrium settling level is always between A and B. The level is linearly proportional to a time-weighted average of the high and low states. (2) The effective time constant t(eff) varies hyperbolically with duty cycle. For DC = (1/3) and t1 = 100 days, the effective time constant is lengthened to 300 days. An asymptote is encountered under certain circumstances where t(eff) approaches infinity. (3) Effective time constants and steady state equilibria are independent of square wave frequency f, animal time constant t1, magnitude and sign of A & B, and diurnal sequencing of the highs and lows. By presenting results on dimensionless coordinates, we can predict the drift rates of some animal experiments. Agreement between theory and experiments has a correlation coefficient r = 0.97 for 12 Macaca nemestrina eyes.

Analogue Computer Model of Progressive Myopia-Refraction Stability Response to Reading Glasses

A tendency of the eye to become myopic with long hours focusing at a near distance has been reported often [1-8]. Myopia development, as any refractive development, is described by a first order feedback system. A first order feedback system is defined by its transfer function F(s) = 1/(1+ks) [1,2]. This function anticipates an exponential development of refractive state and the effect of lenses. Near work is myopizing, as it is equivalent to wearing a negative lens. Using a digital computer, first-order equations have been solved previously to describe and predict myopia progression [1,3]. An analogue circuit can simulate myopia progression vs. time R(t) because the response of the feedback system is the same as the capacitor voltage in a R-C (Resistor-Capacitor) circuit, as shown in Figure 1. When near work is involved a negative square-wave represents the daily accommodative demand as represented in the inset in Figure1[3]. The R-C circuit solves the problem without any computations.

The Progression of Nearwork Myopia

The purpose of this letter is to present a simplified mathematical model of progressive myopia. A proposed hypothesis for refractive error development of the human eye requires that there is an optical signal related to the amount of refractive error which would in turn correct the refractive error of the eye. A specific first-order feedback system, defined by the transfer function F (s) = 1 / (1+ks) [1] was proposed by Medina and Fariza in 1993 [1].