Mathematical Model of Capsule Crack Propagation Trajectory during Continuous Curvilinear Capsulorhexis

During the continuous curvilinear capsulorhexis (CCC) procedure in cataract surgery, an ideally circular and centered capsulorhexis is contributed to the capsular edge perfectly overlapping the intraocular lens (IOL). The anterior lens capsule, as a typical soft material, controlling the propagation of its crack is a critical step in surgery. In this study, to investigate the motion trajectory of the capsulorhexis under a well-centered opening, a mathematical model is proposed to predict the two-dimensional (2D) motion trajectory of the clamping point of the forceps. To analyze the crack propagation, the crack length ratio is defined, and these ratios are obtained for both porcine and human capsules under uniaxial tension and CCC conditions. The mean values for the porcine and human capsules are 1.18 and 1.13 under uniaxial tension, and 1.20 and 1.03 under CCC, respectively. To further refine the theoretical model, we conducted simulated capsule tearing experiments using our ophthalmic robotic platform based on the ex vivo data from the porcine lens capsule and made necessary adjustments. The modified model is then utilized for capsulotomy, and results reveal a diameter error of 8% and a centrality of 0.9 for the torn lens anterior capsule, which validates the feasibility of the proposed trajectory model. Overall, our study provides valuable insights into robot-Assisted automated capsulorhexis for cataract surgery.