Multifocal Intraocular Lens Defocus Profiles Are Best Analyzed With Spline Curves

iol intraocular lens cataract ophthalmology
iol intraocular lens cataract ophthalmology
Researchers concluded that the use of polynomial curve fitting presented too many limitations, according to the report.

Using a spline curve to analyze defocus profiles of intraocular lenses (IOL) is preferable to using single polynomial functions, according to research published in Ophthalmic and Physiological Optics.

Since no standard statistical method exists to determine how well multifocal intraocular lenses (MIOLs) fit,  researchers conducted a study to determine whether 1 polynomial function could fit MIOL and Extended Depth of Focus (EDoF) defocus curves as well as a spline curve.

The team retroscopically reviewed the records of 126 participants who underwent bilateral small incision phacoemulsification and IOL implantation for cataract or elective lens replacement. Patients were fit with 1 of 5 IOLs during the procedure:  monofocal (n=28), diffractive bifocal (n=30), refractive bifocal (n=25), EDoF (n=18), or diffractive trifocal IOL (n=25).

Researchers conducted follow-up visits 3 to 6 months after surgery and determined the best distance correction using retinoscopy and standard subjective refraction. They plotted defocus curves for each participant’s eyes which were corrected for spectacle magnification (SM).

The investigators assessed goodness of fit (GOF) using 5 methods: least squares, coefficient of determination (R2), Akaike Information Criterion (AIC), Snedecor, and Cochrane method and visual inspection.

The team noted different GOF results across the various methods. Snedecor and Cochran methods were consistent across IOLs, but underfit MIOLS and lost information in the intermediate and near sections of the defocus profile. Least squares required 8th order polynomials to fit the IOLs. AIC had more conservative fits compared with R2. However, they established the consistency of the spline curve across all IOLs and methods.

“This study could not establish a conclusive method for choosing a polynomial fit, nor could it establish an order that suited all the IOL types tested sufficiently,” according to the researchers. “Given the variability of results that this study found in relation to polynomial fitting, we advocate selecting the polynomial order for each individual subject according to the adjusted R2, as other goodness of fit strategies are simply too conservative in these circumstances. Even with this individualized approach, particular care and attention must be paid to guard against over/underfitting. The results demonstrated that the use of spline curves is preferred over polynomial curve fitting as it avoids the limitations of polynomial fits.”

Study limitations include dissimilarities in demographic data among the cohort and a lack of ocular biometry data.

Disclosure: This research was supported by Medicontur Medical Engineering. Some of the study authors declared affiliations with biotech, pharmaceutical, and/or device companies. Please see the original reference for a full list of disclosures.


Law EM, Buckhurst HD, Aggarwal RK, et al. Optimising curve fitting techniques to look for standardisation of the analysis of defocus curves derived from multifocal intraocular lenses. Ophthalmic Physiol Opt. Published online April 11, 2022. doi:10.1111/opo.12986