Mechanical Response of Poro-viscoelastic Hydrogel under Tumor Growth at Large Scale and Long Timescale

Introduction: Tumor growth mechanically reshapes the microenvironment of surrounding tissue, changing the mechanical properties of the nearby extracellular matrix (ECM), which may further affect the mechanobiology of native cells and immunotherapies. Tumor growth results in large deformations over a long time scale. However, most deformation tests on matrix networks are done at small strains (≤10%) and short time scales of seconds to minutes, which are not representative of the tumor growth process. As the tumor expands, the adjacent network deforms and experiences stress relaxation, characterized by poroelasticity and viscoelasticity. Viscoelasticity accounts for stress relaxation through matrix rearrangement and dominates in a short timescale of seconds, while poroelasticity explains stress relaxation through fluid transport and is dominant in a long timescale of minutes and hours (Fig1A). Both mechanical properties are present in biological tissues and combined to poro-viscoelasticity. Poroelasticity is particularly interesting as it affects fluid flow, which is important for nutrient trafficking, cell signaling, and cytokine release from immune cells, together affecting the tumor microenvironment. Investigating the mechanical impacts of tumor growth on the surrounding matrix may provide potential insights into strategies and effectiveness of immunotherapy.

The objective of this work is to investigate the mechanical response of the surrounding ECM in tumor growth by applying large deformations at long time scales on a poro-viscoelastic network.

Materials and

Methods: To address the objectives, alginate hydrogel is chosen due to its nanoporous network simulating compact space in tissue. Large deformations are simulated with 40% and 80% compressions, and strain rates from 1%/s to 0.025%/s compare differences in mechanical responses under short and long time scales.

The poro-viscoelastic gel is prepared using low MW alginate with ionic crosslinks connected by Ca2+, and poroelastic gel is prepared using functionalized norbornene (Nb) and tetrazine (Tz) alginate with covalent crosslinks from NbTz click chemistry. Both gels (1.5wt%) are pre-gelled into discs (8mm diameter * 2mm thickness) for 4 hrs and preconditioned in ultrapure water for 24 hrs. Under water-immersed conditions on rheometer HR30, ionic alginate and covalent NbTz gels are compressed at different strain rates (1%/s, 0.25%/s, 0.025%/s) with and without stepwise stress relaxation. Tests with stepwise stress relaxation are done by sequential 10% compression followed by 2500s of stress relaxation. This process is repeated till 40% compression (Fig1B). For each relaxation, time constants are obtained by fitting to the Generalized Maxwell Model. For each compression, the compressive modulus is obtained from linear regression and normalized with the compressive modulus of the first 10% compression. Tests without relaxation are directly compressed to 80% (Fig1D).

Results, Conclusions, and Discussions: For stepwise-relaxed compression on ionic alginate gel, relaxation time constants for strain rates of 0.25%/s and 1%/s are about 100s for the first relaxation, while the time constant for 0.025%/s is 300s. Time constants for the lowest strain rate (0.025%/s) are consistently larger than those for faster strain rates throughout compression. In comparison with poroelastic NbTz gel under fast (0.25%/s) and slow (0.025%/s) strain rates, poro-viscoelastic alginate gel tested at slow rate exhibits a similar time constant as that of poroelastic NbTz gel, which indicates poroelastic behavior dominates at slow strain rates (Fig1C). This may suggest large deformation and stress from tumor growth are mostly dissipated by fluid transport in the surrounding extracellular matrix instead of the viscoelastic response of matrix rearrangement.

For unrelaxed compression, gels were compressed continuously till 80%. Ionic alginate gel tested at 0.025%/s has a long linear region, and strain-stiffening doesn’t occur until 40% (Fig1D). In the axial loading of stepwise-relaxed compression, sudden changes in compression slope are observed after the first relaxation. Here, the first slope is named as E, and the second slope as E+. Comparing compression with and without stepwise relaxation at the low strain rate, we found that E+ matches with slope of unrelaxed compression before 40%, which is without strain-stiffening (Fig1E). Normalized E+ moduli for 0.025%/s strain rate remain at low ratios of 1-1.4, while normalized E+ for 0.25%/s strain rates increase significantly to ratios of 3 as strain increases (Fig1F). This indicates that the slow strain rate and stress relaxation process allow the matrix to repetitively show the same initial compressive modulus even after large compression and long relaxation.

Altogether, low strain rates and long timescale relaxations promote poroelasticity to dominate mechanical responses and allow the network to maintain initial compressive modulus over large deformations. These results suggest the distinct mechanical behavior of ECM under biologically relevant low strain rates and large strains, extending our understanding of strain-stiffening and viscoelastic ECM responses beyond typical fast oscillatory shear tests performed under small deformations (≤10%).

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