Predicting Lens Diameter: Ocular Biometry With High-Resolution MRI

Abstract

Purpose: The aim of this study was to correlate different biometric dimensions of the eye as measured from ocular magnetic resonance imaging (MRI) scans to predict the lens diameter.

Methods: High-resolution ocular MRI scans of 100 eyes of 100 patients were reviewed. Various anatomical variables of the eye such as the axial length, the globe diameter, and the lens dimensions were measured. Also, the distances between the ciliary sulcus and angle-to-angle were measured. A partial least square (PLS) regression model was built to analyze which variables influence the model regarding the lens dimensions.

Results: Sixty-two eyes of 62 patients were included in the final analysis. The lens diameter ratio (horizontal to vertical) was 0.93 (SD: 0.04; 0.83–1.00). The partial least square regression showed a significant connection (P < 0.001) between the horizontal and vertical diameter. The partial least square regression model that included the globe diameter and the axis length resulted in the best prediction for the horizontal lens diameter. Similar to the horizontal lens diameter, globe diameter was the best predictor for the vertical lens diameter followed by the distance of the ciliary sulcus. White-to-white distance, distance of the ciliary sulcus, and axial eye length were found to have a high influence on the angle-to-angle distance.

Conclusions: The introduced models may serve as tools to predict the capsular bag biometry in a preoperative setting for cataract surgery or lens refilling procedures.

Optical biometry together with accurate intraocular lens (IOL) power calculation is key to success to achieve an emmetropic outcome after cataract surgery. Parameters, such as axial eye length and anterior chamber depth (ACD), can be measured very accurately,¹ and measurements of the cornea are improving rapidly.² Another important parameter is the size of the capsular bag, which may have a significant influence on the postoperative IOL position, which remains to be the main source of error in IOL power calculation.³ Furthermore, the ratio between overall diameter of the IOL and the diameter of the capsular bag is crucial for postoperative IOL rotation, which is of clinical relevance in toric IOLs.⁴ Additionally, knowledge of all dimensions of the capsular bag could help to predict postoperative tilt and decentration, which is important for all IOLs, but especially for multifocal, aspherical, and toric IOLs. Optical biometry only allows measurement of lens thickness, but not the diameter of the capsular bag. In vivo measurements of the capsular bag have been performed previously, and it was shown that parameters such as axial eye length are not ideal to predict the diameter of the capsular bag; however, a regression formula was developed to predict very large or very small capsular bags in a preoperative setting.⁵ Postmortem studies showed that the empty capsular bag is 10.0 to 10.8 mm.^6–10 But none of these studies found an acceptable model to predict the capsular bag diameter using preoperative measurements. 

Technical advances in magnetic resonance imaging (MRI) technology led to improved image quality, which is of particular importance for delicate anatomy such as that of the eye. Image resolution improved dramatically over the last few years, without substantial prolongation of the scan time. Recent experimental studies on animals allowed the delineation of retinal layers of the mouse, the rat, and the cat.^11–13 Measurements of the lens dimensions with MRI have been performed previously,¹⁴ but to our knowledge no algorithm for lens diameter prediction was developed. 

The aim of this study was to use a sophisticated MRI set-up to collect MRI biometry data of nonoperated eyes and to use this data set to create a model to predict the capsular bag diameter using parameters that can easily be measured preoperatively. 

Materials and Methods

Patients

High-resolution ocular MRI data of 100 eyes of 100 patients was retrieved from our digital picture archiving system and reviewed. Reasons for referral included the diagnostic work-up of various ocular and orbital mass lesions, as well as inflammatory lesions or trauma. Also, high-resolution ocular MRI was used to determine the irradiation fields to plan proton-beam therapy in uveal melanoma (n = 27). Exclusion criteria were any anatomical changes of the orbit, or the intraocular structure due to the lesion or trauma of the included eye, as well as an age of below 18 years. 

The institutional review board approved the retrospective measurements on the high-resolution ocular MRI data of 100 patients (Ethikkommission Charité - Universitätsmedizin Berlin, No: EA4/009/15). 

Imaging Technique

Magnetic resonance imaging scans were acquired using a 3-Tesla system equipped with a gradient system with a maximum gradient amplitude of 45 mT/m and a maximum slew-rate of 200 mT/m/ms (MAGNETOM Skyra, Siemens Health Care, Erlangen, Germany). A single-channel 7-cm loop surface coil was used in 90 patients and applied over the affected eye. A 20-channel head coil was applied in 10 patients. The conventional ocular imaging protocol included a T1-weighted turbo spin-echo scan in the transverse plane (TR 650 ms, TE 9.1 ms, slice thickness 2 mm [no gap], matrix 208 × 256, field of view 81 × 100 mm, one excitation, voxel size = 0.3894 * 0.3906 * 2 mm, acquisition time 2:58 minutes) and a T2-weighted turbo spin-echo sequence in the transverse plane (TR 3500 ms, TE 69 ms, slice thickness 1 mm [no gap], matrix 156 × 192, field of view 64 × 79 mm, one excitation, voxel size = 0.4103 * 0.4116 * 1 mm, acquisition time 3:30 minutes). 

Image Analysis

All images were analyzed by two experienced radiologists independently from each other. In a second step, data between both readers were compared and in the case of a deviation, a consensus was met. The measurements were performed with the software Visage 7 (VISAGE IMAGING, Inc., Berlin, Germany). 

Qualitative Analysis

The quality of the T1- and T2-weighted images was assessed on a scale in consensus by the two radiologists (0 = no distortion artefact; 1 = minor distortion artefact, anatomy clearly visible; 2 = moderate distortion artefact, anatomy blurred; 3 = major distortion artefact, anatomy not visible). 

Quantitative Analysis

The diagnostic conclusions of the radiology report were documented for each patient. It was documented whether there were signs (such as edema) of a local anaesthetic injected close to the eye to reduce movements during imaging. Also, it was documented whether there was retinal or choroidal detachment. All distances were recorded in millimeters (mm), except the shape factor (SF), which was reported in degrees (°). The anatomical axial length (ALanat) and the maximum axial length (ALmax) were measured from the anterior surface of the cornea to the center of the optic disc and as the maximum measurable length of the globe to the region of the macula excluding the choroid. To obtain these measurements, the T1-weighted images have been selected due to the bright signal intensity of the choroid. Also the T1-weighted images were selected to obtain the white-to-white (WTW) measurements since the transition of the sclera to the cornea (limbus) is clearly visible as a change of signal intensity. 

Central corneal thickness (CCT) as the distance between the anterior and posterior corneal surface in the corneal center as well as the ACD was defined as the distance between the anterior corneal surface and the anterior lens surface were measured on the T2-weighted images. The distances between the ciliary sulcus (DSC) and angle-to-angle (ATA) were identified on the T1-weighted images since the ciliary body and the iris could be best identified in T1 due to its bright signal. 

All the lens measurements (horizontal, vertical, and thickness; LH, LV, LT) were determined on the T2-weighted sequence due to its high contrast between the lens and the vitreous body. The vertical lens diameter (LV) was measured at sagittal reformatted T2-weighted images. Also, the diameter of the globe (BD) as measured from equator to equator, as well as the SF as measured the angle between the equator, the posterior pole, and the opposite equator were defined on T2-weighted images. 

Representative images of the measurements are given in Figures 1 through 3. 

Figure 1

 

T1-weighted images without and with measurements (AL_anat, AL_max, WTW, ATA, DSC).

Figure 2

 

T2-weighted images without and with measurements (CCT, ACD, LT, LH, BD, SF).

Figure 3

 

T2-weighted images reconstructed in the sagittal plane without and with measurements (LV).

Statistical Analysis

For statistical analysis, Microsoft Excel 2011 for Mac (Microsoft, Redmond, WA, USA) with a Statplus:Mac version 5.8.3.8 plug-in (AnalystSoft, Walnut, CA, USA) and a Xlstat 2012 plug-in (Addinsoft, New York, NY, USA) were used. For missing data, observations were excluded from analysis. Descriptive data are always shown as mean, standard deviation (SD), and range. 

For statistical modeling, partial least square (PLS) regression was performed with Xlstat 2012. Advantages of PLS regressions are explained elsewhere¹⁵; here we only want to introduce the main outcome variables of PLS regression: variable importance for projection (VIP) measures the importance of an explanatory variable to explain the dependent variable (more precisely: not the dependent variables, but the t-scores that contain compressed explanatory variables). More relevant for clinicians are the suggested thresholds of the VIPs¹⁶: VIP of >0.8 to <1.0 means that the explanatory variable moderately influences the model and values of 1.0 or more mean that it highly influences the regression model. To evaluate the regression model, a bootstrap method was used to estimate the weighting of each explanatory variable. The result of this boot strapping method is shown in standardized coefficients (= β coefficients) plots. For interpretation purposes, the larger the absolute value of a coefficient, the larger the weight of the variable and if the confidence interval (whiskers) includes 0, the weighting of the variable is not significant. Scatter plots were used to show the correlation of the observed and the predicted dependent variables. 

Results

Quantitative and Qualitative Analysis

Out of 100 eyes of 100 patients, 62 eyes of 62 patients were included in this analysis. Seven cases had to be excluded due to the following reasons: In three cases the quality of the MRI scan was not adequate for analysis, and in four cases the shape of the globe was altered (one case corneal compression, two cases globe compression due to a tumor, and in one case a pars plana vitrectomy was performed prior to the MRI scan). The image quality of the remaining 93 patients was rated 0 in 89 patients (no distortion artefact) and rated 1 in 4 patients (minor distortion artefact, anatomy still clearly visible). None of the imaging data was rated as 2 or 3 (moderate or major distortion artefact, anatomy blurred or not visible) that would have led to exclusion from analysis. 

Ten cases underwent cataract surgery prior to the MRI measurement, and these eyes were also excluded from analysis. Additionally, in 14 cases a retinal and in one case a choroidal detachment and in one case a large melanoma with contact to the lens were documented. Furthermore, parabulbar anaesthesia was applied in five of the remaining cases. All these cases were excluded from analysis and the number of remaining eyes was 62. The final analysis included patients with orbital cancer (e.g., lymphoma) and ocular cancer (uveal melanoma). However, none of these lesions affected the measurements. 

Mean age of the remaining 62 patients was 58.0 years (SD: 14.7; range, 21–79) and female to male distribution was 28:34. All biometric data are shown in Table 1. Central corneal thickness measurements were not included in the analysis since reliability may be poor compared to the other anatomical parameters. 

Table 1

 

Descriptive Data of the Measurements Are Indicated as Range (Minimum, Maximum), Median, Mean, and SD (n = 62)

 

Intra- and interobserver repeatability was tested in the following way: Three parameters (ALmax, WTW, and bulb diameter) of 10 different patients of our data set were measured by the two different radiologists 10 times independently (on 10 consecutive days). The measurements were averaged and compared. ALmax and bulb diameter indicated a very low intraobserver variability (Reader 1: mean ALmax = 23.6 mm [mean SD = 0.1 mm], mean bulb diameter = 25.8 mm [mean SD = 0.1 mm]; Reader 2: mean ALmax = 23.9 mm [mean SD = 0.1 mm], mean bulb diameter = 25.4 mm [mean SD = 0.1mm]). The intra- and interobserver variability of WTW was higher (Reader 1: mean WTW = 10.8 mm [mean SD = 0.3 mm]; Reader 2: mean WTW = 11.9 [mean SD = 0.4]). This higher variability is explained by the gradual, and not abrupt, change of signal between sclera and cornea (limbus) within the T2-weighted images. 

Lens Diameter

The lens diameter ratio (LH/LV) was 0.93 (SD: 0.04; 0.83–1.00). The partial least square regression showed a significant connection (P < 0.001) between both parameters:  

 

 

In all cases, the vertical diameter was found to be larger compared to the horizontal diameter (mean difference, 0.7 mm; SD: 0.43; range, 0.0–1.8 mm, or: 7.5%; SD: 4.90%, range, 0.0%–20.0%), respectively. This difference was found to be significant (Wilcoxon signed rank test: P < 0.001). 

Horizontal Lens Diameter

As shown in Figures 4a and 4b, BD and AL were found to be the best parameters to predict LH.  

 

 

Figure 4

 

Predicting the horizontal lens diameter (LH) by a PLS regression model (a) and the bootstrapping model (b).

Correlation between different parameters and LH are shown in Table 2. 

Table 2

 

Correlation Between Different Parameters and LH

 

Vertical Lens Diameter

Similar to the horizontal lens diameter, globe diameter was the best predictor, but followed by DSC, age, and LT, respectively (Figs. 5a, 5b). 

Figure 5

 

Predicting the vertical lens diameter (LV) by a PLS regression model (a) and the bootstrapping model (b).

Correlation between different parameters and LV are shown in Table 3. 

Table 3

 

Correlation Between Different Parameters and LV

 

Shape Factor

Although globe diameter, CCT, and WTW distance were found to be relevant predictive parameters for the SF of the eye in the PLS regression model, none of these parameters was confirmed in the bootstrapping model. 

ATA Distance

Three parameters were found to have a high influence on the ATA distance, WTW distance, DCS, and axial eye length. All three parameters were also confirmed in the bootstrapping model. However, as the DCS is usually not measureable directly, we show the regression model only using WTW and axial eye length (Fig. 6).  

 

 

Figure 6

 

Prediction of the ATA distance using axial eye length and WTW distance. The thin gray lines show the 95% confidence interval of the mean.

Distance of the ciliary sulcus ATA distance, axial eye length, and globe diameter were found to have the highest influence on the DCS, but the predictive power was not as high as for the ATA. 

Discussion

In this study, ocular biometric measurements were taken from high-resolution MRI scans to develop a model to predict the lens diameter. This prediction model was found to highly correlate with the measured lens dimensions. 

For this study, a sophisticated high resolution MRI set-up was used together with a small surface coil or a head coil, as explained previously.¹⁷ The accuracy of MRI measurements is mainly determined by the image resolution, which was similar compared to other research groups.^14,18,19 Previously, MRIs were used in ophthalmic research mainly to describe anatomical structures¹⁴ and morphologic changes during physiological changes, such as accommodation,^18–21 but not to develop a prediction model for the lens diameter. Richdale et al.²¹ provided quantitative measurements of the lens and ciliary muscle in vivo and demonstrated age-related changes in crystalline lens size and shape. Furthermore, MRI was able to demonstrate changes with advancing age within the ciliary muscle and the lens described by Strenk et al.²² Although other measurement techniques were found to be useful to measure the lens,^5,23 we decided to use MRIs. Vass et al.⁵ used a capsular tension ring that was implanted during cataract surgery. Postoperatively, a gonioscopy lens was used to assess the overlap or the gap of the endings of the capsular tension ring inside the capsular bag to calculate the circumference of the capsular bag. Although this method was shown to be accurate, it was not feasible for this study; however, a correlation between capsular bag diameter and axial eye length and corneal power to identify eyes with large capsular bags was established. Modesti et al.²³ used ultrasound biomicroscopy to evaluate the capsular bag size and accommodative movement before and after cataract surgery. Although feasibility was shown to be high, the study did not show any statistical correlation between alignment of the ciliary apex and capsular bag and accommodative capacity. 

All included patients received a MRI due to lesions or trauma. However, it was taken care of that the included eye (only one eye per patient) did not suffer from anatomical changes concerning the shape of the globe, or the intraocular structures. Patients' data sets that showed signs of peribulbar anesthesia were excluded from the final analysis. However, ElKhamary et al.²⁴ observed the effect of different peribulbar anaesthesia techniques, and they did not observe any morphologic changes of the globe in their MRIs, but it has to be mentioned that their focus of the study was the peribulbar region. 

Also, patients who underwent cataract surgery or who showed retinal or choroidal detachment were excluded from the final analysis. In the first attempt, we wanted to include pseudophakic eyes to test the capsular bag diameter differences between pseudophakic and phakic eyes, but the analysis was not conclusive and the number of pseudophakic eyes was too small. For a better understanding of capsular bag changes due to cataract surgery, it would be necessary to measure patients before and after cataract surgery, similar to the setting of Modesti et al.,²³ but including MRI instead of ultrasound. 

The mean lens diameter in this study (mean LH = 9.03 ± 0.32; mean LV = 9.70 ± 0.48) was found to be similar to observations by Strenk et al.²² (8.92 ± 0.037) and by Richdale et al.²¹ (9.42 ± 0.24). 

Best predictors for the horizontal lens diameter were the globe diameter and the axis length. Similar to the horizontal lens diameter, globe diameter was the best predictor for the vertical lens diameter. This novel prediction algorithm may result in a prediction algorithm. All these parameters can be assessed easily preoperatively with optical biometry. When assessing the predictive power for the lens diameter for each exploratory variable separately, the BD was found to have the highest impact for the horizontal and the vertical diameter. Without knowing the BD, the prediction model suffers significantly and it loses its significance. Further important variables are AL (for LH) and age, as well as DSC (for LV), respectively. There are previous studies to develop a model to predict the lens diameter: Vass et al.⁵ found a positive but weak correlation between axial eye length and capsular bag diameter and a negative and low correlation between corneal power and capsular bag diameter. Modesti et al.²³ measured the capsular bag before and after cataract surgery using ultrasound. They observed a horizontally stretched and vertically reduced capsular bag diameter after cataract surgery. These changes mostly depend on the postoperative position of the IOL and the original size of the capsular bag. 

Rozema et al.²⁵ proposed a multiple linear regressions using common biometric parameters and a moderate correlation between the predicted and the measured lens parameters were found. In their regression approach, multiple linear regression was used, which has some disadvantages. One of them is that multiple linear regression assumes that all explanatory variables are independent from each other. This is not the case for anatomical structures in the eye. Partial least squares regression takes the interaction and dependency of different variables into account and is, therefore, a more appropriate method.²⁶ 

The capsular bag diameter depends on the degree of filling. Assia et al.⁸ reported an increase of the capsular bag diameter of approximately 10% after removal of the lens substance and collapse of the capsular bag in postmortem eyes. Filling of the capsular bag with a viscoelastic material restored the configuration of the lens to its original state. This is the reason why the capsular bag diameter is reported slightly larger in postmortem studies than in MRI studies. However, it is likely that these changes also occur during and after cataract surgery, although to a smaller extent. 

One limitation of the study may be that all regression formulas were based on measurements by MRI and at this stage the level of agreement between the MRI data and those provided by optical biometers that are used in clinical practice is not investigated. Another limitation is that myopic eyes were not included in the study (maximum ALanat = 24.8 mm); therefore, the model may be used in myopic eyes with caution. 

In summary, this study offers a useful prediction algorithm for the lens diameter with variables that can be measured with optical biometry and B-Scan ultrasound. This prediction could be used in the future to improve the prediction of IOL position, the main source of error in IOL power calculation. Furthermore, it could be used to customize the overall diameter of toric IOLs to reduce the risk of postoperative IOL rotation. Additionally, this paper shows that the conventional idea of “long eyes have a large capsular bag diameter” is not always true and can be replaced by this PLS regression model. 

Acknowledgments

Supported by the Rahel Hirsch Program funded by the Charité-Universitätsmedizin Berlin (KE-E). The authors alone are responsible for the content and writing of the paper. 

Disclosure: K. Erb-Eigner, None; N. Hirnschall, None; C. Hackl, None; C. Schmidt, None; P. Asbach, None; O. Findl, None