# Enhancing Brain–Computer Interfaces through Kriging-Based Fusion of Sparse Regression Partial Differential Equations to Counter Injection Molding View of Node Displacement Effects

## TL;DR

This paper introduces a new method using Kriging models and PDEs to optimize injection molding parameters for brain-computer interface components, significantly improving node displacement and signal transmission.

## Contribution

The novel contribution is the fusion of Kriging-based modeling with sparse regression PDEs to optimize BCI manufacturing parameters.

## Key findings

- Optimized injection parameters reduced node displacement from 0.19 mm to 0.89 µm with a 95.32% improvement.
- Key optimized parameters include holding pressure of 525 MPa, holding time of 50 s, and melting temperature of 285 °C.
- The method ensures stable signal transmission and improves BCI system performance.

## Abstract

IME technology is combined with conductive PET and LSR polymer materials to preform Utah arrays for BCI.The effects of three key factors on the nodal displacement were analyzed using the Kriging model.The heat transfer during injection molding was further analyzed by PDEs in order to determine the parameters more accurately.The allowable variation range of the wire diameter is obtained by the relation between the wire diameter and the current.

IME technology is combined with conductive PET and LSR polymer materials to preform Utah arrays for BCI.

The effects of three key factors on the nodal displacement were analyzed using the Kriging model.

The heat transfer during injection molding was further analyzed by PDEs in order to determine the parameters more accurately.

The allowable variation range of the wire diameter is obtained by the relation between the wire diameter and the current.

Injection molding is an efficient and precise manufacturing technology that is widely used in the production of plastic products. In recent years, injection molding technology has made significant progress, especially with the combination of in-mold electronics (IME) technology, which makes it possible to embed electronic components directly into the surface of a product. IME technology improves the integration and performance of a product by embedding conductive materials and functional components in the mold. Brain–computer interfaces (BCIs) are a rapidly growing field of research that aims to capture, analyze, and feedback brain signals by directly connecting the brain to external devices. The Utah array, a high-density microelectrode array, has been widely used for the recording and transmission of brain signals. However, the traditional fabrication method of the Utah array suffers from high cost and low integration, which limits its promotion in practical applications. The lines that receive EEG signals are one of the key parts of a brain–computer interface system. The optimization of injection molding parameters is particularly important in order to effectively embed these lines into thin films and to ensure the precise displacement of the line nodes and the stability of signal transmission during the injection molding process. In this study, a method based on the Kriging prediction model and sparse regression partial differential equations (PDEs) is proposed to optimize the key parameters in the injection molding process. This method can effectively predict and control the displacement of nodes in the film, ensure the stability and reliability of the line during the injection process, and improve the accuracy of EEG signal transmission and system performance. The optimal injection parameters were finally obtained: a holding pressure of 525 MPa, a holding time of 50 s, and a melting temperature of 285 °C. Under this condition, the average node displacement of UA was reduced from the initial 0.19 mm to 0.89 µm, with an optimization rate of 95.32%.