ABSTRACT

Three-dimensional 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 three-dimensional 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.

摘要

使用合成超材料来模拟生物组织的 3D 打印医疗原型在紧急手术应用中变得越来越重要。然而，由于输入（超材料结构）和输出（机械响应曲线）的功能特性，通过 3D 打印超材料模拟组织机械性能可能既困难又耗时。为了解决这个问题，我们提出了一种新的函数对函数克里金模型，用于高效仿真和组织模拟优化。对于函数输入，我们模型的一个关键新颖之处是光谱距离 (SpeD) 相关函数，它捕获了两个函数输入之间的重要光谱差异。然后通过共同克里金法框架对功能输出的依赖性进行建模。我们进一步在输入谱和输出协同克里金协方差矩阵上采用收缩先验，这允许仿真器学习并结合重要的物理特性（例如，主导输入频率、输出曲线属性）。最后，我们证明了所提出的 SpeD 模拟器在模拟人类主动脉组织的真实世界研究中的有效性，并表明与医学文献中的现有方法相比，它可以提供更快、更准确的组织模拟性能。