Function-on-Function Kriging, With Applications to Three-Dimensional Printing of Aortic Tissues
Function-on-Function Kriging, With Applications to Three-Dimensional Printing of Aortic Tissues
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DOI：
10.1080/00401706.2020.1801255
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发表时间：
2019-10
期刊：
影响因子：
2.5
通讯作者：
Jialei Chen;Simon Mak;V. R. Joseph;Chuck Zhang
中科院分区：
文献类型：
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作者：
Jialei Chen;Simon Mak;V. R. Joseph;Chuck Zhang
摘要三维打印医疗原型，它使用合成的超材料来模拟生物组织，在紧急外科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）两者的功能性质，经由三维打印的超材料模仿组织机械特性可能是困难且耗时的。为了解决这个问题，我们提出了一种新的功能上的功能克里格模型，有效的仿真和组织模仿优化。对于功能输入，我们模型的一个关键新奇是光谱距离（SpeD）相关函数，它捕获了两个功能输入之间的重要光谱差异。然后，通过协同克里格框架对功能输出的重复性进行建模。我们进一步在输入光谱和输出协克里格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学（例如，主输入频率、输出曲线特性）。最后，我们证明了所提出的SpeD仿真器在模拟人体主动脉组织的真实世界的研究中的有效性，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。
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.