Characterizing Poroelasticity of Biological Tissues by Spherical Indentation: An Improved Theory for Large Relaxation

Flow of fluids within biological tissues often meets with resistance that causes a rate-and size-dependent material behavior known as poroelasticity.Characterizing poroelasticity can provide insight into a broad range of physiological functions,and is done qualitatively in the clinic by palpation.Indentation has been widely used for characterizing poroelasticity of soft materials,where quantitative interpretation of indentation requires a model of the underlying physics,and such existingmodels are well established for cases of small strain and modest force relaxationWe showed here that existing models are inadequate for large relaxation,where the force on the indenter at a prescribed depth at long-time scale drops to below half of the initially peak force.We developed an indentation theory for such cases of large relaxation,based upon Biot theory and a generalized Hertz contact model.We demonstrated that proposed theory is suitable for biological tissues(e.g.,spleen,kidney,skin and human cirrhosis liver)with both small and large relaxations.The proposed method would be a powerful tool to characterize poroelastic properties of biological materials for various applications such as pathological study and disease diagnosis.

Characterizing in situ poroelastic properties of cytoplasm by the translation of a rigid spherical inclusion

Poroelasticity of cytoplasm is a rate-and size-dependent biphasic material behavior that reflects the normal activities and pathological states of cells,mainly caused by the migration of fluid molecules and the deformation of porous solid skeleton(protein scaffold).While micro/nano-indentation tests have been extensively used to characterize the poroelasticity of a cell,characterizing the in situ poroelasticity of cytoplasm remains elusive.In this study,based on the theory of the translation of a rigid spherical inclusion,we proposed a new method to characterize the in situ poroelasticity of cytoplasm.Based on data from optical/magnetic tweezers tests,we estimated three key poroelasticity parameters-shear modulus,Poisson ratio and diffusion coefficient-of cytoplasm for a variety of cells,including cardiomyocytes,endothelial cells of bovine capillary,and fibroblasts.The proposed method provides a powerful tool for in situ measurement of poroelastic properties of cytoplasm via optical/magnetic tweezers.

A theory of mechanobiological sensation:strain amplification/attenuation of coated liquid inclusion with surface tension

Cells are compressible and can be regarded as a kind of coated liquid inclusion embedded in a three-dimensional elastic matrix.In the presence of far-field loading,how the coating influences the mechanical response(e.g.,volume change)of the liquid inclusion remains elusive,especially when surface tension effects become significant at cell size level.We developed a theoretical model to characterize the mechanical amplification or attenuation role of coating on spherical liquid inclusions,with surface tension and liquid compressibility accounted for.We found that surface tension could increase the volumetric strain of the inclusion through decreasing its effective bulk modulus.We further found that,when there is a monotonic stiffness variation(either decreasing or increasing)from matrix via coating to inclusion,the presence of coating amplified the volumetric strain compared with the case without coating;in the opposite,when there is a non-monotonic stiffness change from matrix via coating to inclusion,the volumetric strain is attenuated by the coating.The results are useful for understanding and exploring the mechanobiological sensation of certain types of cell,e.g.,osteocytes and cancer cells.