Adaptive Temporal Mixture of Experts for Predicting Stiffness Metrics From the Ocular Response Analyzer and Identifying Keratoconus

PURPOSE

To develop a machine learning–based modeling approach for extracting elastic stiffness estimates from Ocular Response Analyzer (ORA) waveforms.

DESIGN

Prospective observational cohort study with model training and testing using a development dataset and validation with an independent validation dataset.

METHODS

Participants were prospectively enrolled into 6 cohorts for the development dataset, including control subjects, individuals diagnosed with keratoconus, diabetes mellitus with retinopathy and without retinopathy, primary open-angle glaucoma, and ocular hypertension. An independent validation dataset comprised data for two cohorts, including healthy participants and individuals diagnosed with keratoconus. Intraocular pressure and biomechanical data were collected using the ORA and Corvis ST devices for the development dataset. An Adaptive Temporal Mixture of Experts (AT-MoE) model, incorporating long short-term memory (LSTM) networks with dynamic expert selection, was trained using ORA waveform parameters and raw signals to predict stiffness parameters (SP) from Corvis ST, including SP-A1 representing corneal stiffness, SP-HC representing scleral stiffness, and SSI representing deformation stiffness. Predicted ORA stiffness estimates were independently validated with a separate dataset of keratoconus and healthy eyes. The ORA waveform parameters, as well as applanation and pressure signals, were used as input to the machine learning models to classify eyes with keratoconus versus healthy eyes, which was evaluated with the area under the receiver operating characteristic (AUROC) curves. The primary outcome measures were the predicted ORA stiffness estimates, including corneal stiffness estimate, scleral stiffness estimate, and deformation stiffness estimate.

RESULTS

The AT-MoE model significantly outperformed the baseline LSTM in predicting ocular stiffness estimates using ORA input data with reduction of prediction error. The AT-MoE model also resulted in improvement of keratoconus detection performance in the independent validation dataset with AUROC $= 0.9512$ , which is similar to performance of tomographic detection approaches.

CONCLUSIONS

The AT-MoE model provides a novel and accurate framework for deriving elastic stiffness estimates from ORA waveforms, and offers improved diagnostic capability for keratoconus compared to traditional machine learning models. This method has the potential to expand the utility of the ORA device for biomechanical assessment in clinical settings.

K eratoconus is a progressive corneal ectasia characterized by focal thinning and steepening of the cornea. Irregular astigmatism and eventual scarring lead to loss of vision and quality of life. Early detection of keratoconus is critical in order to implement interventions that slow progression and preserve vision through normalization of the cornea and scar prevention. ^, Currently, keratoconus is diagnosed by clinical examination in conjunction with topographic or tomographic imaging of the cornea to detect focal thinning and compensatory steepening. This repetitive process leads to the proposed cyclic biomechanical decompensation of the cornea that is initiated by localized weakening at the location where the cone subsequently develops. Thus, clinical biomechanical assessment of corneal elasticity can supplement imaging approaches to allow for the earliest detection. ^,

Currently, clinical evaluation of corneal elastic stiffness parameters is made using the Corvis ST. Although various diagnostic indices have been developed to optimize the diagnostic capabilities of this device, it is not commonly found in primary eye care clinics, where keratoconus is often first detected and diagnosed. Moreover, the biomechanical assessment software does not have approval from the United States Food and Drug Administration (FDA), limiting its use to measurements of intraocular pressure (IOP) and central corneal thickness (CCT) in the United States. Thus, there is a need to develop metrics of corneal elasticity in an FDA-approved device.

The Ocular Response Analyzer (ORA) is a dynamic bidirectional air-puff tonometer that currently provides two measurements of IOP and corneal hysteresis (CH), a viscoelastic biomechanical parameter that quantifies the ability of the cornea to dissipate energy. Although CH is lower in eyes with keratoconus compared to healthy eyes, substantial overlap between the two groups limits its diagnostic potential. However, parameters that describe the pressure–applanation waveforms may provide additional biomechanical information about the cornea. These waveform parameters are altered in glaucoma and are blunted in keratoconic eyes with a central cone. Their diagnostic utility to detect keratoconus, particularly early disease, remains unclear, in part because interpretation of these complex waveforms requires advanced analytical tools capable of capturing both short-term fluctuations, such as the rapid applanation peaks, and long-term trends, such as the overall shape across the entire air-puff, which is influenced by scleral support and global ocular response. Therefore, advanced analytical techniques are needed to generate stiffness estimates from ORA waveforms that can be used to supplement keratoconus detection before vision impairment occurs.

Traditional machine learning models, such as long short-term memory (LSTM) networks, have shown promise in capturing temporal dependencies in sequential data. LSTMs are designed to address the vanishing gradient problem, making them effective for learning from sequences. However, they often have difficulty modeling diverse temporal dependencies across different scales, as they typically learn a fixed set of representations that are not easily specialized for different parts of the sequence. Recent advances in biomedical and ophthalmic imaging analysis have demonstrated the potential of deep learning frameworks to overcome similar limitations in complex data domains. ^,^,^, Mixture of Experts (MoE) models provide a modular learning paradigm in which multiple expert networks are trained to specialize on different parts of the input space, with a gating network determining how to combine their outputs. This approach has been widely explored for the classification of biomedical and ophthalmic data, particularly where spatial or temporal heterogeneity poses challenges for traditional monolithic models. Early model-based frameworks demonstrated the effectiveness of expert-driven strategies in visualizing classification decisions for patient diagnosis and spatial modeling of corneal shape. ^,^,^, These works highlighted the value of decomposing complex spatial patterns into interpretable subcomponents, thereby improving classification accuracy in corneal imaging and videokeratography data. Inspired by these advances, the Adaptive Temporal Mixture of Experts (AT-MoE) model is designed to handle complex sequential data by leveraging modularity and dynamic routing based on the temporal context of the data. This approach allows the model to efficiently capture diverse temporal patterns across multiple timescales, such as short-term fluctuations in corneal deformation and long-term changes in corneal and scleral stiffness.

The purpose of this study was to generate elastic stiffness estimates based on ORA waveform parameters and pressure–applanation waveforms to predict Corvis ST stiffness parameters by developing a novel AT-MoE model to combine the temporal modeling capabilities of LSTM networks with the modular and sparse routing principles of MoE. The generated ORA stiffness estimates will be evaluated in a second independent validation dataset to classify individuals with keratoconus versus healthy subjects.

METHODS

Subjects in the existing development dataset in this cohort modeling study had been prospectively enrolled at The Ohio State University (OSU) Wexner Medical Center under an approved OSU Institutional Review Board protocol, and signed informed consent with Health Insurance Portability and Accountability Act (HIPPA) compliance prior to enrollment. Subjects in the existing validation dataset had been prospectively enrolled at OSU College of Optometry under a separate approved OSU Institutional Review Board protocol, and signed informed consent with HIPPA compliance prior to enrollment. Acquisition protocols differed, with the development dataset embedded within a comprehensive multi-condition research workflow, whereas the validation dataset followed a streamlined clinical protocol. ORA devices were independently maintained and operated by different clinical personnel. These differences introduce natural variability and support the external generalizability of the model. Both protocols were conducted in accordance with the tenets of the Declaration of Helsinki for research on human subjects. Both existing datasets were part of separate larger investigations of ocular biomechanics.

DEVELOPMENT DATASET

The development dataset comprised subjects collected prospectively across 6 cohorts: normal, keratoconus, diabetes without retinopathy, diabetes with retinopathy, ocular hypertension, and glaucoma. These cohorts included a variety of ocular conditions, providing a comprehensive representation of different levels of corneal stiffness and ocular pathologies. This broad range from the lowest stiffness in keratoconus to the highest stiffness in ocular hypertension was essential to ensure the robustness and generalizability of the model in various clinical scenarios. Inclusion criteria across cohorts included a clear cornea, the ability and willingness to comply with the study protocol, and an age of 18 years or older. Exclusion criteria across cohorts included the following: any comorbidity in the pathologic cohorts; nonintact epithelium; pregnancy; less than 12 weeks postpartum or from cessation of breast feeding; nystagmus; previous ocular surgery, except cataract extraction greater than 3 months prior to the date of enrollment; systemic disease that causes defects in collagen, such as Marfan syndrome; and for the normal cohort, a history of ocular disease or trauma.

Cohort eligibility and demographic data

The cohorts were as follows:

•
Normal (NRL): Subjects with normal ocular health, providing baseline data for comparison with the other groups.
•
Keratoconus (KCN): Individuals with a diagnosis of keratoconus with clinical signs, including at least one of reduced corneal thickness, steepening, Fleischer ring, Vogt striae, or scissoring. The focal weakening that generates focal thinning and steepening of the cornea in keratoconus made this an important group in which to study the relationship between corneal stiffness and ocular parameters.
•
Diabetes (DIA): Individuals diagnosed with diabetes, but limited to those without retinopathy. Participants included both type 1 and type 2 diabetes. Diabetes can affect corneal biomechanics, because tissue stiffening occurs in the presence of hyperglycemia.
•
Diabetic retinopathy (DR): Subjects diagnosed with diabetic retinopathy. Participants included both type 1 and type 2 diabetes, but were limited to those with nonproliferative diabetic retinopathy of mild to moderate grade in the absence of macular edema. Diabetic retinopathy may influence scleral stiffness and other ocular parameters.
•
Ocular hypertension (OHT): Individuals in this cohort had elevated intraocular pressure but no signs of glaucomatous damage. This group was relevant for studying corneal and scleral stiffness changes that may protect the optic nerve from glaucomatous damage.
•
Glaucoma (GLA): Subjects with diagnosed primary open-angle glaucoma, a condition associated with progressive optic nerve damage and loss of visual function. Glaucoma patients often exhibit altered corneal and scleral stiffness, which is also affected by topical prostaglandin analogues as one of the pressure-lowering medications, making them a critical group for modeling stiffness metrics. ^,

All subjects with both Corvis ST data and ORA data were extracted from the larger dataset for a total of 961 eyes of 502 subjects in 6 cohorts. Demographic and biomechanical data for the development dataset are given in Table 1 .

TABLE 1

Demographic and Biomechanical Characteristics of Cohorts in Development Dataset.

Development Dataset Cohorts	n (Eyes)	n (Subjects)	Age (y)	IOPcc (mm Hg)	SP-A1 (mm Hg/ mm)	SP-HC (mm Hg/ mm)	SSI	CH (mm Hg)
Normal controls	397	198	39 ± 14	15 ± 3	122 ± 18	14.6 ± 3.9	1.11 ± 0.2	10.6 ± 1.5
Keratoconus	87	54	35 ± 12	14 ± 3	83 ± 22	9.4 ± 3.1	0.88 ± 0.2	8.2 ± 1.5
Diabetes	147	75	49 ± 14	15 ± 3	123 ± 15	14.9 ± 3.2	1.19 ± 0.19	10.8 ± 1.7
Diabetes with retinopathy	146	78	51 ± 14	16 ± 4	128 ± 16	17.1 ± 4.8	1.23 ± 0.22	11.6 ± 2.0
Glaucoma	101	53	61 ± 13	17 ± 4	126 ± 18	15.2 ± 4.4	1.22 ± 0.22	9.5 ± 1.9
Ocular hypertension	83	44	62 ± 17	21 ± 5	143 ± 17	23.0 ± 7.1	1.43 ± 0.27	10.3 ± 2.0

CH = corneal hysteresis; IOPcc = corneal-compensated intraocular pressure; SP-A1 = stiffness parameter at first applanation; SP-HC = stiffness parameter at highest concavity; SSI = stress–strain index.

Values are presented as mean ± SD.

Devices

Corvis ST (Oculus): The Corvis ST is an advanced dynamic tonometer that uses high-speed imaging of the cornea deformation response to an air pressure pulse with consistent spatial and temporal magnitude profiles. Data exported included the biomechanical deformation response parameters of Stiffness Parameter at First Applanation (SP-A1), shown to represent corneal response; Stiffness Parameter at Highest Concavity (SP-HC), shown to represent scleral response ; and StressStrain Index (SSI), which was developed via finite element modeling and represents deformation stiffness response. These parameters are important for understanding the relationship between intraocular pressure and ocular response, which includes both the cornea and sclera.

Ocular Response Analyzer (Reichert Technologies): The ORA is used to assess corneal biomechanical response to an air pressure pulse that is customized so that an eye with lower IOP receives a lower-magnitude pulse and an eye with higher IOP receives a higher-magnitude pulse. This air-puff strategy is one feature that differentiates the ORA from the Corvis ST. A second feature that differentiates them is the electro-optical detection system used by the ORA to track corneal displacement, explained in the next section. The ORA data in the development dataset of the current study is a second-generation device (G2). Data were exported from the ORA G2 examination with the highest waveform score of the three examinations performed, and included corneal compensated intraocular pressure (IOPcc), corneal hysteresis (CH), waveform parameters, and both pressure/applanation signals, to be described in the next section.

ORA waveform parameters

The ORA produces two signals by projecting an infared (IR) beam onto the cornea and collecting the diffuse reflection from the corneal surface. One signal represents the air pressure magnitude versus time, and the other represents the photons collected by the IR photodetector versus time, which spikes at both inward and outward applanation events due to a mirror-like reflection of the IR light that maximizes the light captured by the aligned detector. This second signal is called the applanation response curve; it tracks the spatial deformation information by the amount of light collected as a function of the angle of the light impinging on the detector as the corneal surface is displaced. The magnitude of the applanation signal reaches a local minimum between the two rapid applanation events and represents the maximum corneal displacement. A series of 44 waveform parameters are exported that correspond to various aspects of the corneal deformation response in the recorded signal. The waveform parameters describe the shape and characteristics of the pressure-response waveforms, for example, the heights and widths of the two applanation peaks shown in Figure 1 .

Data splitting

Those subjects who had both ORA data and Corvis ST data ultimately populated the development dataset. The total dataset of 502 subjects was split into training and testing subsets by subject. Any subject included in the training set was excluded from the testing set. The training set consisted of $80 %$ of the data, whereas the remaining $20 %$ was reserved for testing. Training, testing, and validation sets were strictly separated, ensuring no overlap of eyes from a given individual across partitions. Feature selection and normalization statistics were computed exclusively on the training set and subsequently applied to test and validation sets without recalculation, thereby eliminating the risk of data leakage.

ORA stiffness estimates

•
Corneal stiffness estimate (CSe): This metric corresponds to the Stiffness Parameter at First Applanation (SP-A1) from the Corvis ST. CSe reflects the resistance of the cornea to deformation from the initial convex shape to the flattened state at applanation. It is considered a key indicator of corneal stiffness and is relevant in conditions such as keratoconus with low corneal stiffness and diabetes with high corneal stiffness.
•
Scleral stiffness estimate (SSe): This metric corresponds to the Stiffness Parameter at Highest Concavity (SP-HC) from the Corvis ST. Scleral stiffness reflects the resistance of the sclera to aqueous displacement during the concave phase of deformation from applanation to the limit of corneal concavity when the sclera is fully engaged. Scleral stiffness also influences the overall biomechanical response of the ocular shell to IOP and is particularly important in the study of glaucoma and ocular hypertension.
•
Deformation stiffness estimate (DSe): This metric corresponds to the Stress–Strain Index (SSI) from the Corvis ST, which uses finite element modeling of corneal deformation to the highest concavity in order to determine corneal stiffness. DSe provides useful insights into the cornea’s deformation response to internal and external pressures, especially in diseases that affect corneal structure.

DATA PREPROCESSING

The preprocessing of the dataset was a crucial step to ensure the quality and effectiveness of the model. The waveform parameters, which include several time-series measurements from the ORA, were subjected to normalization techniques to standardize the data and to remove any inherent biases due to differences in scale or range.

Normalization of waveform parameters

To standardize the waveform parameters across all subjects and cohorts, each parameter was normalized using max–min scaling. This technique transforms the values of each feature to a $[0, 1]$ range based on the minimum and maximum values observed for that specific parameter across the dataset. This ensures that each feature contributes equally to the model’s learning process, thereby preventing parameters with larger scales from dominating the model’s performance.

The formula for max–min scaling is as follows:

X_{norm} = \frac{X - min (X)}{max (X) - min (X)}

where

X

is the original value of a parameter, and

X_{norm}

is the normalized value.

Normalization of pressure and applanation curves

The pressure and applanation curves, which represent time-series data obtained from the ORA, were also normalized independently for each subject. This normalization was necessary because these curves can have varying magnitudes between subjects, potentially distorting the learning process if not properly adjusted.

Each pressure and applanation curve was normalized to the range $[0, 1]$ by using the following max–min scaling procedure:

X_{norm} (t) = \frac{X (t) - min (X)}{max (X) - min (X)}

where

X (t)

represents the value at time step

t

in the curve, and

X_{norm} (t)

is the normalized value for that specific time point.

FEATURE SELECTION

To select the top waveform parameters most relevant to the prediction of the stiffness estimates, a carefully designed data preprocessing pipeline was used to extract the most relevant waveform parameters for the prediction of three stiffness values: scleral stiffness estimate (SSe), corneal stiffness estimate (CSe), and deformation stiffness estimate (DSe). This preprocessing pipeline combined statistical, machine learning, and optimization techniques to construct subsets of top features tailored to each stiffness value. The selected top waveform parameters included the following:

IOPg, CRF, IOPcc, p2area, p2area1, w21, CH, path1, path2, w11.

Hybrid feature selection approach

The original dataset consisted of 44 waveform parameters. Selecting a compact and informative feature set required addressing two key challenges: namely, identifying parameters that are jointly relevant to all three stiffness estimates, and avoiding redundancy among highly correlated waveform descriptors. Therefore, a hybrid feature selection approach was developed to identify a single common subset of waveform parameters used for predicting all three stiffness targets.

Multi-target statistical relevance estimation: For each waveform parameter $X_{i}$ , its dependence on each stiffness estimate $Y_{k} \in {SSe, CSe, DSe}$ was quantified using mutual information (MI), which captures both linear and nonlinear relationships:

M I (X_{i}, Y_{k}) = \int \int p (X_{i}, Y_{k}) log (\frac{p (X_{i}, Y_{k})}{p (X_{i}) p (Y_{k})}) d X_{i} d Y_{k}

To obtain a single relevance score per waveform parameter that reflects its overall association with all stiffness estimates, MI values were aggregated across targets:

Relevance (X_{i}) = \frac{1}{3} \sum_{k = 1}^{3} M I (X_{i}, Y_{k})

This multi-target relevance score favors parameters that consistently capture biomechanical information across corneal, scleral, and deformation stiffness.

Feature diversity maximization using optimization: To reduce redundancy among selected parameters, feature diversity was enforced using a maximal relevance–minimal redundancy (MRMR) criterion. Redundancy between two waveform parameters $X_{i}$ and $X_{j}$ were quantified using cosine similarity:

Redundancy (X_{i}, X_{j}) = \frac{X_{i}^{⊤} X_{j}}{∥ X_{i} ∥ ∥ X_{j} ∥}

Feature selection was formulated as the following optimization problem:

max_{S \subseteq F, | S | = k} (\sum_{X_{i} \in S} Relevance (X_{i}) - λ \sum_{X_{i}, X_{j} \in S} Redundancy (X_{i}, X_{j})),

where

F

denotes the full set of waveform parameters,

S

is the selected feature subset,

k = 10

, and

λ

controls the trade-off between relevance and redundancy.

The optimization was solved using a greedy forward-selection strategy, in which features were iteratively added to $S$ based on their marginal contribution to the objective. This procedure resulted in a single common set of 10 waveform parameters that was used as input for all stiffness prediction tasks.

Normalization and sequence construction

After feature selection, the selected waveform parameters for each stiffness value were normalized using z -score normalization:

{\hat{X}}_{i} = \frac{X_{i} - μ (X_{i})}{σ (X_{i})}

where

μ (X_{i})

and

σ (X_{i})

are the mean and standard deviation of parameter

X_{i}

across the training data.

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Tags: American Journal of Ophthalmology Volume 286

Sep 20, 2026 | Posted by drzezo in OPHTHALMOLOGY | Comments Off

Ento Key

Fastest Otolaryngology & Ophthalmology Insight Engine

Adaptive Temporal Mixture of Experts for Predicting Stiffness Metrics From the Ocular Response Analyzer and Identifying Keratoconus

PURPOSE

DESIGN

METHODS

RESULTS

CONCLUSIONS

METHODS

DEVELOPMENT DATASET

Cohort eligibility and demographic data

Devices

ORA waveform parameters

Data splitting

ORA stiffness estimates

DATA PREPROCESSING

Normalization of waveform parameters

Normalization of pressure and applanation curves

FEATURE SELECTION

Hybrid feature selection approach

Normalization and sequence construction

Related

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Ento Key

Fastest Otolaryngology & Ophthalmology Insight Engine

Adaptive Temporal Mixture of Experts for Predicting Stiffness Metrics From the Ocular Response Analyzer and Identifying Keratoconus

PURPOSE

DESIGN

METHODS

RESULTS

CONCLUSIONS

METHODS

DEVELOPMENT DATASET

Cohort eligibility and demographic data

Devices

ORA waveform parameters

Data splitting

ORA stiffness estimates

DATA PREPROCESSING

Normalization of waveform parameters

Normalization of pressure and applanation curves

FEATURE SELECTION

Hybrid feature selection approach

Normalization and sequence construction

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