Facile Tuning of the Mechanical Properties of a Biocompatible Soft Material

Abstract
Herein, we introduce a method to locally modify the mechanical properties of a soft, biocompatible material through the exploitation of the effects induced by the presence of a local temperature gradient. In our hypotheses, this induces a concentration gradient in an aqueous sodium alginate solution containing calcium carbonate particles confined within a microfluidic channel. The concentration gradient is then fixed by forming a stable calcium alginate hydrogel. The process responsible for the hydrogel formation is initiated by diffusing an acidic oil solution through a permeable membrane in a 2-layer microfluidic device, thus reducing the pH and freeing calcium ions. We characterize the gradient of mechanical properties using atomic force microscopy nanoindentation measurements for a variety of material compositions and thermal conditions. Significantly, our novel approach enables the creation of steep gradients in mechanical properties (typically between 10–100 kPa/mm) on small scales, which will be of significant use in a range of tissue engineering and cell mechanosensing studies.

Introduction
Gradients of mechanical properties are found in innumerable natural systems and phenomena and at all length scales1,2,3. The behaviour of cells cultivated on substrates of different stiffness have been widely studied in recent years, unveiling how migration4,5,6, proliferation6,7, adhesion5,8 and also differentiation7,9,10 are dependent on the characteristics of the material upon which the cells proliferate. To date most of these studies have considered materials of defined but uniform rigidity, with few assessing biocompatible materials possessing a rigidity gradient11,12,13. This is relevant, for example, for the osteotendinous insertion, the tissue formed by differentiations of Mesenchymal Stem Cells (MSCs) that connects the soft tendinous and the rigid osseous tissue. This is characterised by a gradient of stiffness responsible for the differentiation of the stem cells14. In this respect, control over the Young’s modulus of such materials is extremely limited. Herein, we show for the first time the creation, tuning and control of mechanical property in biocompatible materials by inducing a concentration gradient through the application of thermophoretic forces. Significantly, the ability to impose and control temperature gradients across a microfluidic channel allows facile manipulation of elasticity gradients in the final material.

Two major challenges faced when generating rigidity gradients relate to the availability of polymers that permit the formation of the desired gradient in mechanical property and the accessibility of formation methodologies. Unsurprisingly, both issues are closely related, with biocompatibility requirements further complicating the undertaking.

Traditionally, the rigidity of a gel can be tuned by controlling the degree of crosslinking or the initial monomer concentration. For example, the use of an optical mask containing a spatial gradient in transparency can be used to control light intensity during the photo-polymerization process12. Alternatively, a microfluidic gradient generator15 and a photo-polymerization step can be used to “fix” a desired concentration gradient within a material. Nevertheless, the main limitations of such techniques relate to the choice of the substrate material, which is restricted to UV curable polymers, and reduced control over the magnitude of the rigidity gradient.

To address the aforementioned limitations, we herein exploit the possibility to accurately impose and control a temperature gradient within a microfluidic device to create a novel class of biocompatible material presenting a rigidity gradient, based on crosslinked calcium alginate constrained within microfluidic geometries. In the presence of a temperature gradient, the solutes dispersed in solution are affected by thermophoresis which induces the formation of a concentration gradient. Here we suggest a mechanism based on the combined effect of the thermophoretic drift of each component dispersed in the aqueous solution of sodium alginate to explain the obtained results. Significantly, since thermophoresis can be applied to any kind of solute dispersed in solution, the basic method can be easily extended to any polymer or hydrogel undergoing a polymerization or sol-gel process. The main advantage of our proposed approach is the fact that we can effectively decouple the control over the local stiffness of the material from the polymerisation process. By exploiting thermophoresis, we can induce a gradient of mechanical properties that is independent from the choice of the material. For example, the concentration gradient can be gently tuned by thermophoresis in a delicate biocompatible hydrogel using only minute temperature differences that do not alter the overall properties of the material and then, independently, the material can be crosslinked.

Thermophoresis is a physical phenomenon discovered over one century ago16,17. Briefly, in the presence of a temperature gradient, a solute dispersed in solution will migrate along that temperature gradient and accumulate either on the ‘cold’ or the ‘hot’ side depending on the specific solute-solvent interactions18, average temperature19, solute size20,21 or type of dispersed electrolyte22. At steady-state, the mass flux, Jm, is zero and the concentration gradient is counterbalanced by the temperature gradient (Eq. 1), where the gradient is assumed to be along the z-axis, i.e.

$$\begin{array}{ccc}{J}_{m} & = & \rho [D\frac{dc}{dz}-c(1-c){D}_{T}\frac{dT}{dz}]\\ {J}_{m} & = & 0\to \frac{dc}{dz}=-\,c(1-c){S}_{T}\frac{dT}{dz}\end{array}$$ (1)
here, ρ is the density of the solute, c is the concentration, D is the diffusion coefficient, DT is the thermophoretic mobility and ST the so called Soret coefficient, equal to DT/D. In simple terms, the Soret coefficient is positive when solute accumulates on the low temperature side and negative when accumulation occurs on the high-temperature side.

The concentration gradient induced by thermophoresis is proportional to the temperature gradient and, as a consequence, at small scales typical of microfluidic devices, only a very limited temperature difference is required over the biocompatible material to generate the required mechanical properties gradient, and no other material property is influenced by this.

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