High Resolution, Large Deformation 3D Traction Force Microscopy

Abstract

Traction Force Microscopy (TFM) is a powerful approach for quantifying cell-material interactions that over the last two decades has contributed significantly to our understanding of cellular mechanosensing and mechanotransduction. In addition, recent advances in three-dimensional (3D) imaging and traction force analysis (3D TFM) have highlighted the significance of the third dimension in influencing various cellular processes. Yet irrespective of dimensionality, almost all TFM approaches have relied on a linear elastic theory framework to calculate cell surface tractions. Here we present a new high resolution 3D TFM algorithm which utilizes a large deformation formulation to quantify cellular displacement fields with unprecedented resolution. The results feature some of the first experimental evidence that cells are indeed capable of exerting large material deformations, which require the formulation of a new theoretical TFM framework to accurately calculate the traction forces. Based on our previous 3D TFM technique, we reformulate our approach to accurately account for large material deformation and quantitatively contrast and compare both linear and large deformation frameworks as a function of the applied cell deformation. Particular attention is paid in estimating the accuracy penalty associated with utilizing a traditional linear elastic approach in the presence of large deformation gradients.

3D Viscoelastic traction force microscopy

“…As can be seen from Fig. 8, the utilization of the 3D VTFM methodology produces high-resolution traction maps with similar resolution and sensitivity capabilities to our previously published 3D large deformation elastic TFM approach 18 .…”

“…Cell-generated full-field displacements were determined following a similar methodology described in Tojanova et al 18 . First, three-dimensional time-lapse volumetric images of fluorescent beads embedded in agarose substrates were recorded using laser scanning confocal microscopy (LSCM).…”

“…The surface normal vectors can be determined directly from the laser scanning confocal images. Toyjanova et al previously described such a method in-detail 18 . The magnitude of the three-dimensional traction vector is then calculated as $$\left|\mathrm{boldt}\right|\sqrt{t_x^2+t_y^2+t_z^2},$$ where t x and t y are the in-plane traction force components under the cell and t z corresponded to the out-of-plane component.…”

“…Yet, until recently, almost every TFM approach featured a linear elastic continuum mechanics framework 15–17 . Through a recent significant advancement in our displacement detection scheme we showed that cells on soft gels are capable of generating large material deformations exceeding the traditional linear formulation limits 18 . We addressed these observations by presenting a new, reformulated hyperelastic 3D TFM approach, capable of accurately capturing finite elastic material deformations 18 .…”

For whom the cells pull: Hydrogel and micropost devices for measuring traction forces

“…Such characteristics limit the use of 3D TFM for analyzing fast traction force measurements of contractile activities involved in cell motility [34, 35] and beating of cardiomyocytes [36, 37]. These methods can also be extended to estimate traction stresses for cells embedded in 3D environments using digital volume correlation algorithms [25, 29, 38, 39]. …”