3D low frequency electromagnetic modelling of the human eye with boundary elements: Application to conductive keratoplasty

Conductive keratoplasty (CK) is a non-ablative surgical technique for the treatment of mild to moderate hyperopia (far-sightedness). In a CK session a thin electrode penetrates the cornea and delivers pulsed radio-frequency energy at 350kHz to the surrounding tissue. The electromagnetic (EM) energy is dissipated into heat in the tissue surrounding the tip yielding thermally localised shrinkage and tightening of the collagen lamellae. When applied in a controlled way, this relatively new technique allows eye surgeons to correct the shape of the cornea and to treat common eye types of disease such as far-sightedness or astigmatism. The purpose of this work is to present a three-dimensional boundary element model of the human eye and its solution for the current density distribution in the different tissues when exposed to CK treatment. This is in order to examine in detail the induced currents that appear in the rest of the eye while delivering the EM signal, and to understand how the human eye behaves as a bulk imperfect conductor when a low frequency high voltage signal is locally applied. The Boundary element method is implemented with a multi-domain staggered approach in which each boundary element contains both continuous and discontinuous nodes. The former allocate electric potential only, while the latter allocate normal electric field only. In this way, continuity of the potential is ensured between adjacent elements and the complication of matching normal electric fields at corner points generated by elements of different orientations is avoided. A quantitative estimation of the EM energy absorbed in each tissue is presented, as well as the initial impedance of the electrodes.