An Analytical Approach to Corneal Mechanics for Determining Practical, Clinically-Meaningful Patient-Specific Tissue Mechanical Properties in the Rehabilitation of Vision

Abstract

Patient-specific biomechanical properties of the human cornea are rarely used with finite elements analysis. In order for that to be possible, a proper formulation for biomechanical properties that is based on patient-specific measurable values must be used. In this study, we propose a formula that simulates hyperelastic stress-strain curves based on non-invasive clinical measurements that can be acquired in vivo. These consist of, but are not limited to, center corneal thickness and center corneal curvature as well as corneal resistance factor and applanation diameter that are measured during non-contact tonometry. The presented formulation was demonstrated and validated through several computer simulations. First, mean values that were reported in literature were inputted into the formula to simulate a curve that represents a healthy case. This case was compared to two independent in vitro studies. Then, a sensitivity analysis was carried to identify inputs that have the most dominant effect. Finally, a finite element analysis simulating elevations in intraocular pressure was conducted; the corneal model comprised of patient-specific corneal geometry that was measured in vivo in our clinic as well as the current formulation for patient-specific corneal biomechanics. "Strong" and "weak" corneal tissue cases were simulated and deformations as well as instantaneous curvature optical maps were derived. Results for the simulated healthy curve showed good agreement with the in vitro studies. The sensitivity analysis found the corneal resistance factor and applanation diameter to have the most dominant influence. The finite element analysis of strong and weak biomechanical properties resulted in corneal deformations and instantaneous curvature optical maps that are common for healthy and pathological conditions respectively. In conclusion, the presented modeling technique can be used to assess corneal biomechanics in vivo and therefor may enhance follow-up on the effectiveness of clinical treatments, rehabilitation of vision and perhaps improve the diagnosis of pathologies that are related to corneal biomechanics.

A Study for Parametric Morphogeometric Operators to Assist the Detection of Keratoconus

“…In the literature, some works that use CAD models integrate the patient-specific model concept, which provides quantitative results applicable to a specific patient [16][17][18][19][20]. This model is obtained from the so called "raw data" [21], which are generated by systems based on the projection of a slit light onto the cornea and on the principle of Scheimpflug photography [5].…”

“…Several works in the finite elements field use these raw data for several purposes: to predict the response to refractive surgeries [19] or the response to the intrastromal ring segment implantation in corneas with keratoconus [18], to analyse non-surgical corneal modifications, such as applanation tonometry for intraocular pressure measurement [20], or to analyse the behaviour of corneal tissue properties in different scenarios [16,17]. In all these cases, raw data were provided by the Pentacam (Oculus Optikgeräte GmbH, Wetzlar, Germany) [16,18], Sirius (CSO, Florence, Italy) [19,20], or Galilei (Ziemer Ophthalmic Systems AG, Port, Switzerland) [17] devices.…”

“…In all these cases, raw data were provided by the Pentacam (Oculus Optikgeräte GmbH, Wetzlar, Germany) [16,18], Sirius (CSO, Florence, Italy) [19,20], or Galilei (Ziemer Ophthalmic Systems AG, Port, Switzerland) [17] devices. However, due to extrinsic errors [5] occurring during the measurement process, the generated raw data were incomplete; thus, the authors of the mentioned works were forced to interpolate with the aim of obtaining a complete representation of the corneal surfaces and, thus, generate a 3D model of the cornea for its posterior use in the finite elements method.…”

“…An alternative to these geometric models are the zonal methods called B-Spline functions [23]. However, this technology is not extended to the ophthalmology field, and it has only been used to generate customised models of the corneal biomechanics [17,18,20]. In these cases, the raw data obtained were incomplete in the periphery and the limbus areas due to extrinsic errors during the data acquisition process, so the authors had to interpolate data in order to obtain a complete geometric model.…”

Assessment of Pattern and Shape Symmetry of Bilateral Normal Corneas by Scheimpflug Technology

“…During the process of generating the corneal topographies and in the preprocessing stage, the Sirius system allows raw data to be exported in comma-separated values (CSV) format, which is the format of the files used herein. Moreover, these files can be obtained from other corneal topographers [20,[22][23][24][25][26], all of them based on the Scheimpflug principle. Therefore, the analysis proposed in this study is compatible with and independent of the commercial equipment used.…”