Physically Consistent Scar Tissue Dynamics from Scattered Set of Data: A Novel Computational Approach to Avoid the Onset of the Runge Phenomenon

The foreign body reaction is a complex biological process leading to the insulation of implanted artificial materials through a capsule of scar tissue. In particular, in chronic implantations of neural electrodes, the prediction of the scar tissue evolution is crucial to assess the implant reliability over time. Indeed, the capsule behaves like an increasing insulating barrier between electrodes and nerve fibers. However, no explicit and physically based rules are available to computationally reproduce the capsule evolution. In addition, standard approaches to this problem (i.e., Vandermonde-based and Lagrange interpolation) fail for the onset of the Runge phenomenon. More specifically, numerical oscillations arise, thus standard procedures are only able to reproduce experimental detections while they result in non physical values for inter-interval times (i.e., times before and after experimental detections). As a consequence, in this work, a novel framework is described to model the evolution of the scar tissue thickness, avoiding the onset of the Runge phenomenon. This approach is able to provide novel approximating functions correctly reproducing experimental data (R2≃0.92) and effectively predicting inter-interval detections. In this way, the overall performances of previous approaches, based on phenomenological fitting polynomials of low degree, are improved.