Lakhasly

Under a Creative Commons license Abstract The Poisson's ratio and elastic modulus are two parameters determining the elastic behavior of biomaterials.Moreover, there is an explicit analytical relationship describing the relationship between the design parameters of hexagonal unit cells and the Poisson's ratio ( of the resulting 2D meta-biomaterial [51]: (1) where and denote the transverse and longitudinal strains, respectively. For instance, in porous scaffolds or implants, the micro-architectural design determines the effective elastic modulus with porosity and pore size serving as critical morphological parameters that need to be tailored to mimic native tissues [12,13].In addition to the effective elastic modulus, the Poisson's ratio (i.e., the negative ratio of the transverse to the longitudinal strain) is a crucial factor in biomaterial design and is known to play a significant role in regulating cell behavior [9,[14], [15], [16], [17]].The outcomes of osteogenic differentiation (i.e., Runx2 immunofluorescent staining) and matrix mineralization (i.e., Alizarin red staining) assays indicated the significant potential impact of these meta-biomaterials in the field of bone tissue engineering, paving the way for the development of advanced bone meta-implants.The 2PP technique creates high-resolution, complex meso-scale structures with micro-metric or sub-micrometric features [45], [46], [47], [48], [49], [50], enabling the creation of 3D scaffolds with varying Poisson's ratios and allowing the study of the impact ofthese properties on the cell behavior in 3D.Subsequently, we measured the mechanical properties of IP-Q at the micro-scale (i.e., a cylinder with equal diameter and height of 30.0 um) for our FEM models using micro-compression, and similarly, characterized the mechanical properties of the meta-biomaterials at the meso-scale to validate our rational design approach.In this study, we first used computational mechanics and the finite element method (FEM) to rationally design meta-biomaterials with different values of the Poisson's ratio (range of - 0.74 to + 0.74) while maintaining similar values of the effective elastic modulus, porosity, pore size, and strut diameter.To tackle this, this study employed rational computational design to craft meta-biomaterials with controlled Poisson's ratios, alongside consistent effective elastic modulus, porosity, and pore size.Graphical Abstract Download : Download high-res image (382KB) Download : Download full-size image Keywords Meta-biomaterials; Poisson's ratio; two-photon polymerization; preosteoblasts; metabolic activity; differentiation 1.Introduction Both the effective elastic modulus of the scaffolds (~stiffness) and the biomaterial's Young modulus may modulate cell fate and subsequent tissue development through mechanotransduction pathways involving cytoskeletal reorganization, and changes in gene expression and protein synthesis[1], [2], [3], [4].Advanced micro-additive manufacturing (micro-AM) techniques, such as two-photon polymerization (2PP), have emerged as a valuable tool for exploring the influence of the Poisson's ratio on cell response in 3D micro-/meso-scale structures [41], [42], [43], [44].Then, we employed the 2PP technique to fabricate these complex meta-biomaterials at the meso-scale (i.e., 1356.0x1356.0x1800.0 um3 with a strut diameter of 36.0 um) using a methacrylate photosensitive polymer (called IP-QTM).The porosity of such meta-biomaterials is defined as: (2) where and respectively refer to the volumes of the meta-biomaterial calculated from a CAD software and the volume of a solid cube encompassing the entire meta-biomaterial structure ( in Figure 1.a.i).Interestingly, the meta-biomaterials exhibited different cell-induced deformations (e.g., shrinkage or local bending) as observed via scanning electron microscopy.Finally, we evaluated the response of mouse preosteoblasts seeded onto the meta-biomaterials by assessing their viability, metabolic activity, spatiotemporal organization, as well as the osteogenic differentiation and matrix mineralization.The complexity arises from intertwined micro- architectural parameters, such as porosity and elastic modulus, making it challenging to isolate the Poisson's ratio.Several strategies can be employed to modulate the effective elastic modulus of scaffolds depending on the targeted tissue, biochemical properties, and manufacturing techniques.The micro-architecture of meta-biomaterials determines not only the Poisson's ratio but also several other parameters that also influence cell response, such as porosity, pore size, and effective elastic modulus.Here, we computationally design metabiomaterials with controlled Poisson's ratios, ranging between -0.74 and +0.74, while maintaining consistent porosity, pore size, and effective elastic modulus.The 3D meta-biomaterials were additively manufactured at the micro-scale using two-photon polymerization (2PP), and were mechanically evaluated at the meso-scale.It is, therefore, necessary to consider the elastic modulus of the target tissue in the design of biomaterials and scaffolds, which can vary greatly from soft tissues (e.g., brain with an elastic modulus of approximately 1-4 kPa [5], [6], [7]) to hard tissues (e.g., cancellous bone with an elastic modulus of around 0.04-1 GPa [6,8]).This offers new opportunities for developing innovative 3D-engineered microenvironments that can be customized for specific tissue engineering and regenerative medicine applications.However, rational design techniques could be used to decouple the Poisson's ratio of meta-biomaterials from their effective elastic modulus and morphological properties.Statement of Significance What's this?Material and methods 2.1.2.

Under a Creative Commons license
Abstract
The Poisson's ratio and elastic modulus are two parameters determining the elastic behavior of biomaterials. While the effects of elastic modulus on the cell response is widely studied, very little is known regarding the effects of the Poisson's ratio. The micro-architecture of meta-biomaterials determines not only the Poisson's ratio but also several other parameters that also influence cell response, such as porosity, pore size, and effective elastic modulus. It is, therefore, very challenging to isolate the effects of the Poisson's ratio from those of other micro-architectural parameters. Here, we computationally design metabiomaterials with controlled Poisson's ratios, ranging between -0.74 and +0.74, while maintaining consistent porosity, pore size, and effective elastic modulus. The 3D meta-biomaterials were additively manufactured at the micro-scale using two-photon polymerization (2PP), and were mechanically evaluated at the meso-scale. The response of murine preosteoblasts to these meta-biomaterials was then studied using in vitro cell culture models. Meta-biomaterials with positive Poisson's ratios resulted in higher metabolic activity than those with negative values. The cells could attach and infiltrate all metabiomaterials from the bottom to the top, fully covering the scaffolds after 17 days of culture. Interestingly, the meta-biomaterials exhibited different cell-induced deformations (e.g., shrinkage or local bending) as observed via scanning electron microscopy. The outcomes of osteogenic differentiation (i.e., Runx2 immunofluorescent staining) and matrix mineralization (i.e., Alizarin red staining) assays indicated the significant potential impact of these meta-biomaterials in the field of bone tissue engineering, paving the way for the development of advanced bone meta-implants.
Statement of Significance What’s this? open access: We studied the influence of Poisson's ratio on bone cell response in meta-biomaterials. While elastic
modulus effects are well-studied, the impact of Poisson's ratio, especially negative values found in
architected biomaterials, remains largely unexplored. The complexity arises from intertwined micro-
architectural parameters, such as porosity and elastic modulus, making it challenging to isolate the
Poisson's ratio. To tackle this, this study employed rational computational design to craft meta-biomaterials
with controlled Poisson's ratios, alongside consistent effective elastic modulus, porosity, and pore size. The
study reveals that two-photon polymerized 3D meta-biomaterials with positive ratios displayed higher
metabolic activity, and cell growth than those with negative values. The outcomes pave the way for the
development of advanced 3D bone tissue models and meta-implant.
Graphical Abstract
Download : Download high-res image (382KB)
Download : Download full-size image
Keywords
Meta-biomaterials; Poisson's ratio; two-photon polymerization; preosteoblasts; metabolic activity;
differentiation

1. Introduction
   Both the effective elastic modulus of the scaffolds (∼stiffness) and the biomaterial's Young modulus may
   modulate cell fate and subsequent tissue development through mechanotransduction pathways involving
   cytoskeletal reorganization, and changes in gene expression and protein synthesis[1], [2], [3], [4]. It is,
   therefore, necessary to consider the elastic modulus of the target tissue in the design of biomaterials and
   scaffolds, which can vary greatly from soft tissues (e.g., brain with an elastic modulus of approximately 1-4 kPa
   [5], [6], [7]) to hard tissues (e.g., cancellous bone with an elastic modulus of around 0.04-1 GPa [6,8]).
   Several strategies can be employed to modulate the effective elastic modulus of scaffolds depending on the
   targeted tissue, biochemical properties, and manufacturing techniques. These strategies encompass a
   variety of factors, including the base material, coating, external stimuli, and geometrical cues [9], [10], [11].
   For instance, in porous scaffolds or implants, the micro-architectural design determines the effective elastic
   modulus with porosity and pore size serving as critical morphological parameters that need to be tailored
   to mimic native tissues [12,13].In addition to the effective elastic modulus, the Poisson's ratio (i.e., the negative ratio of the transverse to
   the longitudinal strain) is a crucial factor in biomaterial design and is known to play a significant role in
   regulating cell behavior [9,[14], [15], [16], [17]]. The Poisson's ratio of architected biomaterials with
   repetitive unit cells is a function of the kinematic design of their underlying mechanisms. This ratio can be
   varied from negative to positive values by rationally adjusting the geometrical designs of the repetitive unit
   cells [18,19]. Mechanical metamaterials offer a promising approach to control the Poisson's ratio while
   keeping the effective elastic modulus unaffected. These materials are a class of advanced engineered
   materials featuring unconventional properties owing to their micro-architectural design [20], [21], [22],
   [23], [24], [25], [26], [27].
   One example of the unusual properties of mechanical metamaterials is the auxetic property or a negative
   Poisson's ratio. Auxetic metamaterials expand transversely when stretched longitudinally and contract
   transversely when compressed longitudinally, which is the opposite of the behavior shown by conventional
   materials [20,[28], [29], [30], [31]]. This unique property can make auxetic materials ideal for use in hybrid
   hip implants, as they can expand on the side of the implant experiencing tension under bending [32]. This
   can solve the current challenges in traditional hip implants which exhibit shrinkage on the tension side and
   expansion on the compression side under such loading conditions. Expansion on the compression side is
   beneficial as it promotes adherence to the surrounding bone and prevents aseptic loosening. However, the
   shrinkage on the tension side may eventually lead to the creation of a gap between the bone and the
   implant, increasing the risk of implant loosening. Auxetic meta-biomaterials could address this problem by
   offering a negative Poisson's ratio on the tension side of such implants, which has been already
   demonstrated as a conceptual design and early prototype [32]. Such a design, therefore, can prevent implant
   loosening and improve the connection between the implant and the surrounding bone [32,33]. Therefore,
   auxetic meta-biomaterials have the potential to offer unique solutions to the challenges faced in the design
   of implantable medical devices [34].
   To better understand the effects of mechanical cues on cell-scaffold interactions, both effective elastic
   modulus and Poisson's ratio must be considered. However, the maximum values of both the Poisson's ratio
   and effective elastic modulus are coupled with each other (Hashin–Shtrikman bounds [35], [36], [37]). The
   effective elastic modulus is coupled with micro-architectural parameters, which makes it challenging to
   change either the morphology or the elastic behavior without affecting the other. However, rational design
   techniques could be used to decouple the Poisson's ratio of meta-biomaterials from their effective elastic
   modulus and morphological properties.
   Recent studies have highlighted the significance of the Poisson's ratio in regulating cell behavior [9,13,17,
   [38], [39], [40]]. For example, negative values of the Poisson's ratio have been shown to differently affect cell
   proliferation [17], differentiation [9], alignment, and directionality, as compared to positive values of the
   Poisson's ratio [16]. However, most research has focused on the effect of the Poisson's ratio in 2D (and 2.5D)
   meta-biomaterials, with only a few studies investigating the impact of the Poisson's ratio in 3D biomaterials
   [9,16,40]. In those studies, however, the interdependence between micro-architectural parameters,
   Poisson's ratio, and effective elastic modulus, has not been sufficiently addressed. Here, we aim at
   elucidating the independent effects of the Poisson's ratio in 3D micro-environments on the response of
   preosteoblast cells.
   Advanced micro-additive manufacturing (micro-AM) techniques, such as two-photon polymerization (2PP),
   have emerged as a valuable tool for exploring the influence of the Poisson's ratio on cell response in 3D
   micro-/meso-scale structures [41], [42], [43], [44]. The 2PP technique creates high-resolution, complex
   meso-scale structures with micro-metric or sub-micrometric features [45], [46], [47], [48], [49], [50],
   enabling the creation of 3D scaffolds with varying Poisson's ratios and allowing the study of the impact ofthese properties on the cell behavior in 3D. Moreover, the availability of chemically biocompatible photoresists make the 2PP technique a potential tool in cell biology studies [42].
   In this study, we first used computational mechanics and the finite element method (FEM) to rationally design meta-biomaterials with different values of the Poisson's ratio (range of - 0.74 to + 0.74) while maintaining similar values of the effective elastic modulus, porosity, pore size, and strut diameter. Then, we employed the 2PP technique to fabricate these complex meta-biomaterials at the meso-scale (i.e., 1356.0×1356.0×1800.0 µm3 with a strut diameter of 36.0 μm) using a methacrylate photosensitive polymer (called IP-QTM). Subsequently, we measured the mechanical properties of IP-Q at the micro-scale (i.e., a cylinder with equal diameter and height of 30.0 µm) for our FEM models using micro-compression, and similarly, characterized the mechanical properties of the meta-biomaterials at the meso-scale to validate our rational design approach. Finally, we evaluated the response of mouse preosteoblasts seeded onto the meta-biomaterials by assessing their viability, metabolic activity, spatiotemporal organization, as well as the osteogenic differentiation and matrix mineralization.
   Our study provides new insights into the importance of the Poisson's ratio, as a mechanical cue in the design of meta-biomaterials. This offers new opportunities for developing innovative 3D-engineered microenvironments that can be customized for specific tissue engineering and regenerative medicine applications.


2. Material and methods
   2.1. Rational design of the meta-biomaterials To determine the optimal parameters for the 3D design of meta-biomaterials, we started off with 2D structures to initially guess the mechanical properties. This approach was advantageous as computational modeling of 2D structures is more straightforward than that of 3D structures. Moreover, there is an explicit analytical relationship describing the relationship between the design parameters of hexagonal unit cells and the Poisson's ratio (
   of the resulting 2D meta-biomaterial [51]: (1) where and denote the transverse and longitudinal strains, respectively. The geometrical parameters , and are illustrated in Figure 1.a.iii. The porosity of such meta-biomaterials is defined as: (2) where and respectively refer to the volumes of the meta-biomaterial calculated from a CAD
   software and the volume of a solid cube encompassing the entire meta-biomaterial structure ( in Figure 1.a.i).