Function-on-function kriging, with applications to 3D printing of aortic tissues

TL;DR

This paper introduces a novel function-on-function kriging model with spectral-distance correlation for efficient emulation of tissue properties in 3D-printed medical prototypes, improving accuracy and speed in mimicking biological tissues.

Contribution

The paper proposes a new spectral-distance correlation function for functional inputs and integrates it into a co-kriging framework with shrinkage priors, advancing tissue-mimicking optimization methods.

Findings

The SpeD emulator outperforms existing methods in accuracy.

The model provides faster tissue-mimicking predictions.

Effective in real-world aortic tissue study.

Abstract

3D-printed medical prototypes, which use synthetic metamaterials to mimic biological tissue, are becoming increasingly important in urgent surgical applications. However, the mimicking of tissue mechanical properties via 3D-printed metamaterial can be difficult and time-consuming, due to the functional nature of both inputs (metamaterial structure) and outputs (mechanical response curve). To deal with this, we propose a novel function-on-function kriging model for efficient emulation and tissue-mimicking optimization. For functional inputs, a key novelty of our model is the spectral-distance (SpeD) correlation function, which captures important spectral differences between two functional inputs. Dependencies for functional outputs are then modeled via a co-kriging framework. We further adopt shrinkage priors on both the input spectra and the output co-kriging covariance matrix, which allows the emulator to learn and incorporate important physics (e.g., dominant input frequencies, output curve properties). Finally, we demonstrate the effectiveness of the proposed SpeD emulator in a real-world study on mimicking human aortic tissue, and show that it can provide quicker and more accurate tissue-mimicking performance compared to existing methods in the medical literature.