CompBioMed23 Publication: Model Order Reduction and Sensitivity Analysis for complex ocular simulations inside the human eyeball

[thomas-saigre]

Model Order Reduction and Sensitivity Analysis for complex ocular simulations inside the human eyeball

Overview

The ocular contribution is devoted to modeling the complex interplay between tissue perfusion, biomechanics, fluid dynamics, and heat transfer within the eye. These different aspects of the same physical problem must be properly connected and every step has to be verified and validated in the interest of a medical application. The models require the knowledge of various parameters; some may be important factors in developing pathologies. However, despite recent advances in medical data acquisition, only some parameters and their variability are known, but others cannot be directly measured. To identify the main factors that influence the biomechanical behavior of the eye, we, therefore, need to study the influence of these parameters through an uncertainty quantification (UQ) process which requires many evaluations of the models.
Since 3D models are not amenable directly to UQ, a reduction step is needed to mitigate the computational cost.

Parameter dependent model

We focus on heat transfer inside the human eyeball. Because of the complexity of the organ, many regions are involved, with different physiological properties.
The exchanges of heat with the surrounding body, as well as the ambient air, are also modeled.

In the model, many parameters are involved, and we want to study the impact of those parameters on the distribution of the temperature.

Solutions for three values of parameters: $\bar{\mu}$ composed of nominal values for a human eyeball, $\mu_\min$ and $\mu_\max$ as extremal values.

Certified reduced basis

The reduced basis method (RBM) allows to building of a surrogate model to simulate the distribution of the temperature over the eyeball, by means of an efficient and stable procedure: we want to replicate the solution while significantly reducing the time of execution.
The RBM ensures the quality of the reduced solution, providing a posteriori error-bound.

For instance, the high fidelity model (with 1 580 932 degrees of freedom) takes 101.81 s to assemble and solve the problem for a given parameter, while the reduced model (of size 10) takes 6.27e-5 s to compute both solution and error bound.

Error on RBM for various reduced basis sizes, represented with the error bound $\Delta_N$, for a sample of 100 parameters

Numerical results

Thanks to the RBM, we can compute the solution for a very large number of parameters, and perform an Uncertainty Quantification, such as compute the Sobol indices.
Sobol indices are indicators of the effect of a parameter on the output of interest.

Sobol indices: temperature at the front of the eyeball

We notice a significant impact of external factors (ambient air temperature $T_\text{amb}$, tear evaporation $E$), and subject-specific data (such as the blood temperature $T_\text{bl}$) on the corneal temperature.

Next steps

• Model: couple thermal effect with aqueous humor dynamics in the anterior chamber,
  
  Aqueous humor dynamic in the anterior chamber
• Non-intrusive reduced basis method with zoom in zone of interest,
• Application: robust framework to simulate drug delivery in the eye.

References

This work has been presented at the CompBioMed2023 conference, held in Munich from 12 to 14 September 2023.
Check out the presentation on the HAL portal.