A Tensegrity-Graph Optimization Framework for Estimating Intracellular Stiffness

In this paper we present a formulation for estimating intracellular stiffness using tensegrity principles. We demonstrate that the new tensegrity model, based on random graphs over dense nodes, can predict well known mechanical characteristics of epithelial and mesenchymal cells.

Study of the Mechanical Behavior of Subcellular Organelles Using a 3D Finite Element Model of the Tensegrity Structure

A tensegrity model can be used to describe the mechanical behavior of living cells. A finite element model (FEM) was used to assess the mechanical contribution of subcellular organelles. Continuum parts like the cytoplasm and membrane were modeled as continuous elements, while the tensegrity was chosen to model the cytoskeleton and nucleoskeleton. An atomic force microscope load was implemented to simulate the external load. The cell components were loaded separately to evaluate their mechanical contributions. The analysis started with a single cytoplasm and each of the cell components was added in consecutive steps. The results showed that the cytoskeleton carried the largest part of the reaction force. The cytoplasm was the second important component of the cell’s mechanical response. It was shown that the nucleoskeleton has a stiffer structure than the membrane and cytoplasm. The cytoskeleton supported approximately 90% of the reaction force, while the cytoplasm carried 9% and the shell parts and nucleoskeleton were responsible for about 1%.

Migration of the 3T3 Cell with a Lamellipodium on Various Stiffness Substrates—Tensegrity Model

Changes in mechanical stimuli and the physiological environment are sensed by the cell. Thesechanges influence the cell’s motility patterns. The cell’s directional migration is dependent on the substrate stiffness. To describe such behavior of a cell, a tensegrity model was used. Cells with an extended lamellipodium were modeled. The internal elastic strain energy of a cell attached to the substrates with different stiffnesses was evaluated. The obtained results show that on the stiffer substrate, the elastic strain energy of the cell adherent to this substrate decreases. Therefore, the substrate stiffness is one of the parameters that govern the cell’s directional movement.

Sensing and Modelling Mechanical Response in Large Deformation Indentation of Adherent Cell Using Atomic Force Microscopy

The mechanical behaviour of adherent cells when subjected to the local indentation can be modelled via various approaches. Specifically, the tensegrity structure has been widely used in describing the organization of discrete intracellular cytoskeletal components, including microtubules (MTs) and microfilaments. The establishment of a tensegrity model for adherent cells has generally been done empirically, without a mathematically demonstrated methodology. In this study, a rotationally symmetric prism-shaped tensegrity structure is introduced, and it forms the basis of the proposed multi-level tensegrity model. The modelling approach utilizes the force density method to mathematically assure self-equilibrium. The proposed multi-level tensegrity model was developed by densely distributing the fundamental tensegrity structure in the intracellular space. In order to characterize the mechanical behaviour of the adherent cell during the atomic force microscopy (AFM) indentation with large deformation, an integrated model coupling the multi-level tensegrity model with a hyperelastic model was also established and applied. The coefficient of determination between the computational force-distance (F-D) curve and the experimental F-D curve was found to be at 0.977 in the integrated model on average. In the simulation range, along with the increase in the overall deformation, the local stiffness contributed by the cytoskeletal components decreased from 75% to 45%, while the contribution from the hyperelastic components increased correspondingly.

Tensegrity Truss Model using Fem Applications

In this paper, tensegrity structures were formulated on truss by the conventional rolled steel members (RS) namely Type 1 truss and by pipe sections namely Type 2 truss. The Type 1 and Type 2 truss structures was modeled and analyzed using software’s (ANSYS and STAADPRO packages). For Type 2 truss, tensegrity model was attained with the self-equilibrium state at various load cases. The members of the truss was designed by IS: 800- 1984 and 2007 methods and compared based on utility ratio. The detailing of Type 1 and 2 trusses were done by TEKLA software. The nodal deflection and member stresses were compared and tabulated by ANSYS and STAADPRO software’s.