Biomedical Engineering Reference
In-Depth Information
range, structural efficiency, viscoelastic behavior) are emergent properties that
arise from the particular architecture used to stabilize the 3D network.
4.1.3. Computational Tensegrity Models Predict Complex Cell Behaviors
If the complex mechanical behaviors of cells, including their global me-
chanical stability, flexibility, ability to remodel, and optimal strength/mass ratio,
represent emergent properties of cell structural networks, then we should be able
to get insight into how this takes place by studying and modeling cytoskeletal
mechanics (60). Existing paradigms assume that the static and dynamic me-
chanical behaviors of living cells respectively originate from two distinct com-
partments—the elastic cortical membrane and the viscous cytoplasm. Recent
work, however, has revealed that cell dynamic behavior reflects a generic sys-
tem property of the cell at some higher level of molecular interaction as it is
characterized by a wide spectrum of time constants (18). Dimitrije Stamenovic,
working with our group (58), and with others (72,73,65,66), have shown that a
theoretical formulation of the cellular tensegrity model based on first mechanis-
tic principles can predict various static mechanical properties of living mammal-
ian cells. More recently, we found that the tensegrity model also can explain
dynamic cell mechanical behaviors, as described below.
The theoretical tensegrity model of the cell is a deterministic physics-based
model which assumes that contractile microfilaments and intermediate filaments
carry a stabilizing tensile prestress in the cytoskeleton that is balanced by inter-
nal microtubule struts and extracellular adhesions. The cytoskeleton and sub-
strate together were assumed to form a self-equilibrated, stable mechanical
system; the prestress carried by the cables is balanced by the compression of the
struts. The simplified tensegrity network used in the computational model is
composed of 24 tensed, linearly viscoelastic (Kelvin-Voigt), "microfilament"
cables and 6 rigid "microtubule" struts; 12 additional tensed Kelvin-Voigt "in-
termediate filament" cables extend from the surface of the structure to the cell
center and the basal ends of 3 struts are fixed to mimic cell substrate adhesion
(Figure 2). Importantly, work on variously shaped models has revealed that even
the simplest prestressed tensegrity network embodies the key mechanical prop-
erties of all prestressed tensegrities (this is the degree of abstraction mentioned
above). In this computational model, the material properties of the tensile fila-
ments can be varied independently. The equilibrium solution around which the
linear mathematical model was derived for frequency response calculations is a
prestressable configuration (63). The prestress is a measure of the tension in the
cables. The input was a vertical, sinusoidally varying force applied at the center
of a strut; the output was its corresponding vertical displacement (Figure 2).
Analysis of the variations of the dynamic elastic modulus
G
' and dynamic
frictional modulus
G
'' with the level of prestress for various frequencies in this
