Why this project exists

Modern cataract surgery frequently uses toric intraocular lenses (IOLs) to correct corneal astigmatism. Choosing the correct cylinder power and axis is critical, small errors can leave patients with residual astigmatism and sub-optimal vision, which can’t be adjusted later.

Today, most toric planning still relies on keratometry:

Cylinder ≈ K2 − K1
Axis ≈ steep meridian

This approach assumes the cornea behaves like a perfect toric surface. Real corneas are not perfect toroids.

Irregular astigmatism, asymmetry, higher-order shape, and measurement noise all reduce the reliability of SimK-based planning.

We asked a simple question:

Can a model learn toric IOL planning directly from the entire corneal shape instead of two keratometry numbers?

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The dataset

We assembled a dataset of corneal topography exams paired with real post-op refractions.

Each sample represented one eye.

Inputs (from topography export)

From device exports (Oculus topographer):

• Axial curvature grid (diopters)

• SimK values and quality indices

The curvature grid is a 2D matrix representing corneal optical power.

Typical size after preprocessing:

128 × 128 matrix of diopters

Targets (ground truth)

Only patients implanted with non-toric IOLs

Because no toric correction was applied, the post-op refractive cylinder represents the true residual corneal astigmatism after surgery. This makes it an ideal target for training a predictive model. It’s also important to note that these results are subjective, so the model will be targeting what the patients feel gives their best vision, not what’s mathematically perfect

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Baseline: How Toric Planning Normally Works

Before building any ML model, I implemented a baseline pipeline replicating the logic of common clinical metrics:

1. Apply a central 3 mm mask to the curvature map

2. Detect steep and flat meridians

3. Compute simulated keratometry (SimK)

4. Convert to predicted cylinder + axis

This serves as the “traditional algorithmic approach.”

(img1)

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Machine Learning Approach

Instead of reducing the cornea to two numbers, I let the model see the entire curvature grid.

Input

• Normalized 2D curvature maps

• Resized to a fixed resolution

• Augmented with rotations and noise

Model Architecture

I used a compact convolutional neural network (CNN) designed for regression.

Outputs:

• Cylinder magnitude

• Astigmatism axis (circular regression)

Training losses:

• Mean absolute error (cylinder)

• Circular angular loss (axis)

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Data pipeline

We built the entire pipeline in Python.

Tools used

Category	Libraries
Data ingestion	pandas, NumPy
DICOM parsing	pydicom
Image processing	OpenCV, SciPy
Machine learning	PyTorch
Evaluation	scikit-learn, SciPy
Visualization	Matplotlib, Seaborn

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Preprocessing steps

Raw exams differ in size, orientation, and noise.

We standardized every corneal map.

1) Centering

Align grid to corneal apex.

2) Masking

Remove invalid pixels from tear-film artifacts.

3) Resizing

Interpolate to 128×128 resolution.

4) Normalization

Standardize diopter values.

Each eye became:

Input: 128×128 curvature map
Target: cylinder (D), axis (°)

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Evaluation Strategy

We compared two predictions against the real post-op manifest refraction:

1. Traditional SimK prediction

2. Machine learning prediction

Metrics:

• Cylinder MAE (diopters)

• Axis circular error (degrees)

• Vector refractive error

We also created a subgroup of complex corneas, defined as:

• Low magnitude (<1D) OR

• Asymmetric/irregular maps

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Results

Overall Performance

Metric	Traditional	ML Model
Cylinder MAE	0.48 D	0.38 D
Axis Error	17.2°	13.6°

This represents a:

20% reduction in prediction error

(img2)

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Performance in Complex Corneas

Metric	Traditional	ML Model
Cylinder MAE	0.57 D	0.37 D

This represents a:

35% improvement in difficult cases

This was the most encouraging result of the study.

(img3)

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Error Distribution

The ML model produced:

• Fewer large outliers

• Tighter error distribution

• More stable axis prediction

(img4)

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Clinical Implications

Even modest improvements matter in toric planning.

A 0.1–0.2D cylinder error reduction can:

• Improve uncorrected visual acuity

• Reduce residual refractive astigmatism

• Increase patient satisfaction

Most importantly:

The largest gains occurred where clinicians struggle most, irregular and ambiguous astigmatism.