An efficient statistical approach to design 3D-printed metamaterials for mimicking mechanical properties of soft biological tissues

Wang, Kan; Zhang, Chuck; Wang, Ben

doi:10.1016/j.addma.2018.10.007

Cited by 19 publications

(16 citation statements)

References 28 publications

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“…Our spectral-distance (or SpeD) correlation captures this physics by assigning a correlation of 1 (i.e., perfect correlation) for these two inputs. On the other hand, previous studies (Wang et al, 2016a;Chen et al, 2018a) showed that spectral differences in metamaterial geometries contribute greatly to variations in mechanical property. The SpeD correlation directly models this physics by measuring the distance between two functional inputs in the spectral domain.…”

Section: Introductionmentioning

confidence: 91%

“…Translation-invariance property for inputs (Chen et al, 2018a) Spectral-distance correlation function Frequency information is important (Chen et al, 2018a) Frequency domain weight function Only a few important frequencies (Chen et al, 2018a) Sparsity in frequency coefficients Separability of geometry and mechanics (Fung, 2013) Separable co-kriging structure Known structure of mechanical response (Callister and Rethwisch, 2011) Sparsity in co-kriging covariance matrix use the following scale-parametrized l 2 distance function in the spectral domain:…”

Section: Physical Properties Model Assumptionsmentioning

confidence: 99%

“…Currently, the state-of-the-art approach is to print sub-structure, or metamaterial (see Figure 1), to mimic the mechanical properties of biological tissue (Wang et al, 2016a,b). However, such a mimicking procedure requires careful tuning, which may take days or even weeks to perform (Chen et al, 2018a). This greatly limits the medical applicability of tissue-mimicking metamaterial, since surgery timing is a critical factor for outcome success.…”

Section: Introductionmentioning

confidence: 99%

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

Chen,

Mak,

Joseph

et al. 2019

Preprint

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3D-printed medical phantoms, 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 geometry) and outputs (its corresponding mechanical response curve). To deal with this, we propose a novel function-on-function kriging emulation model for efficient tissue-mimicking. 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 sparse 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.

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Section: Introductionmentioning

confidence: 91%

Section: Physical Properties Model Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Chen,

Mak,

Joseph

et al. 2019

Preprint

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“…We will consider three design inputs x = (A, ω, d), which parametrize a standard sinusoidal form of the substructure curve I(t) = A sin(ωt), with diameter d (see Fig 2(b) for a visualization). This parametric form has been shown to provide effective tissue-mimicking performance in prior studies (Wang et al, 2016;Chen et al, 2018a). The response of interest ξ(x) is the modulus at strain level of 8%, which quantifies the stiffness at a similar load situation inside the human body (Wang et al, 2016).…”

mentioning

confidence: 99%

“…We start with an n ini = 25-run initial computer experiment design, and then perform n seq = 8 sequential runs using physical experiments. The limited number of sequential runs is due to the urgent demand of the patients; in such cases, only one to two days of surgical planning can be afforded (Chen et al, 2018a). Since physical experiments require tedious 3D printing and a tensile test (around 1.5 hours per run), this means only a handful of runs can be performed in urgent cases.…”

mentioning

confidence: 99%

Adaptive design for Gaussian process regression under censoring

Mak¹,

Joseph²,

Zhang³

2019

Preprint

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A key objective in engineering problems is to predict an unknown experimental surface over an input domain. In complex physical experiments, this may be hampered by response censoring, which results in a significant loss of information. For such problems, experimental design is paramount for maximizing predictive power using a small number of expensive experimental runs. To tackle this, we propose a novel adaptive design method, called the integrated censored mean-squared error (ICMSE) method. Our ICMSE method first learns the underlying censoring behavior, then adaptively chooses design points which minimize predictive uncertainty under censoring. Under a Gaussian process regression model with product Gaussian correlation function, the proposed ICMSE criterion has a nice closedform expression, which allows for efficient design optimization. We demonstrate the effectiveness of the ICMSE design in the two realworld applications on surgical planning and wafer manufacturing.

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A Novel Twofold Symmetry Architected Metamaterials with High Compressibility and Negative Poisson's Ratio

2021

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The advancements in additive manufacturing (AM) technology make the fabrication of complex architected materials and structures at multiple length scales possible to explore a new family of metamaterial. A metamaterial is an artificially engineered material to have a property not found in conventional materials. [1] Historically, the term "metamaterials" were limited to electromagnetism field, but, recently, it has been extended to photonic, phononic, and mechanical systems to design architected engineered materials that exhibit properties not usually found in conventional materials. [2] Mechanical metamaterials refer to a sort of metamaterials that designed artificial structural materials with counterintuitive mechanical properties derived from their tailored internal microstructure rather than the composition of base material. [3] The unusual properties include negative Poisson's ratio, negative modulus of elasticity, and negative compressibility. [4,5] Examples of mechanical metamaterials include acoustic metamaterials, auxetic materials, pentamode metamaterials, and micropolar metamaterials. The concept of metamaterials combined with AM opens new design avenues for the fabrication of complex microstructures over a wide range of length scales. [6][7][8] Auxetic mechanical metamaterials are recognized by a negative Poisson's ratio; i.e., materials will contract (expand) in the transverse direction when compressed uniaxially (stretched). Auxetic mechanical metamaterials are of interest because of their enhanced mechanical properties, such as increased indentation resistance, [9] shear modulus, [10] and fracture toughness. [11] They have a great potential in engineering applications, such as cellular materials with superior damping and acoustic properties, [12] piezoelectric metamaterials, [13] piezocomposites, [14] auxetic fasteners, [15] bioprostheses, [16] tissue engineering, [17] and mechanically tunable, elastically reversible, and transformable topological mechanical metamaterials. [18,19] The negative Poisson's ratio of auxetic material depends on the topology of auxetic building blocks and scaleindependent. [20,21] Several natural materials exhibit negative Poisson's ratio, such as silicates, [22] cubic elemental metals, [23] zeolites, [24] natural layered ceramics, [25] and monolithic ferroelectric polycrystalline ceramics. [26] Love [27] was the first to report the negative Poisson's ratio of naturally occurring cubic crystals of

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An efficient statistical approach to design 3D-printed metamaterials for mimicking mechanical properties of soft biological tissues

Cited by 19 publications

References 28 publications

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

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

Adaptive design for Gaussian process regression under censoring

A Novel Twofold Symmetry Architected Metamaterials with High Compressibility and Negative Poisson's Ratio

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