Adjoint-based inverse determination of shear modulus and intraocular pressure

An elevated intraocular pressure (IOP) is a direct indication of glaucoma---a leading cause of blindness. The feasibility of a new waveform tonometry concept for simultaneous inverse determination of the IOP and the elasticity of human eye is explored in this research. This concept is based on the vibration characteristics of the eye. The biomechanical eye model is described by the boundary value problem of small fluid-structure interaction oscillation superimposed on a static configuration state corresponding to the initial large deformation due to the IOP loading.{09}Since the response of the eye is a function of the elasticity and IOP, it is essential that the elastic moduli are recovered simultaneously with the IOP to render the determination objective. To recover the IOP, an inverse problem is formulated by minimization of a multiple-frequency residual functional which quantifies the deviation of the predicted displacements from the signature profiles. These distinctively different dynamic deformations at multiple frequencies lead to the regularization of the ill-posed inverse problem. A gradient-based algorithm is employed for the minimization, and the sensitivities are calculated by the adjoint method. For the computation of the multiple-frequency solutions and the sensitivities at each functional evaluation step, a full-field matrix-Pade via Lanczos technique is developed and it allows for simultaneous computation of these displacements and adjoint fields with the cost of essentially one factorization. By comparison to the stretching stiffness, the prestress is concluded to be a higher-order term; and its effect on the residual functional is improved by using waveform excitation. Since the prestress is due to the IOP loading, it must be determined to render the problem tractable. A closed-form expression for the prestress function is obtained by using an asymptotic procedure for the corneoscleral shell. Several inversion results are reported. The elastic moduli are accurately recovered, and hence render the IOP an objective measure.