Three-Dimensional Quantification of Cellular Traction Forces and Mechanosensing of Thin Substrata by Fourier Traction Force Microscopy

We introduce a novel three-dimensional (3D) traction force microscopy (TFM) method motivated by the recent discovery that cells adhering on plane surfaces exert both in-plane and out-of-plane traction stresses. We measure the 3D deformation of the substratum on a thin layer near its surface, and input this information into an exact analytical solution of the elastic equilibrium equation. These operations are performed in the Fourier domain with high computational efficiency, allowing to obtain the 3D traction stresses from raw microscopy images virtually in real time. We also characterize the error of previous two-dimensional (2D) TFM methods that neglect the out-of-plane component of the traction stresses. This analysis reveals that, under certain combinations of experimental parameters (\ie cell size, substratums' thickness and Poisson's ratio), the accuracy of 2D TFM methods is minimally affected by neglecting the out-of-plane component of the traction stresses. Finally, we consider the cell's mechanosensing of substratum thickness by 3D traction stresses, finding that, when cells adhere on thin substrata, their out-of-plane traction stresses can reach four times deeper into the substratum than their in-plane traction stresses. It is also found that the substratum stiffness sensed by applying out-of-plane traction stresses may be up to 10 times larger than the stiffness sensed by applying in-plane traction stresses

Didactic strategies for comprehension and learning of structural concepts

p. 926-937In previous papers we have established the convenience of formulating educational strategies at the university level for both disciplines: Civil Engineering and Architecture, which involves academic topics of mutual interest by means of shared practices. As a particular matter of this approach, the application of physical experimental models is considered of special usefulness, in order to understand in better ways the performance of materials and structural systems. Several strategies of selection and development of such physical models will be discussed in this work, considering as a first step, the establishment of its correspondence with the different levels of structural complexity studied in curriculum plan: statics, strength of materials and structural design, among others. This task constitutes a part of the work program of the Laboratory of Structural Models, which is an academic project that develops and applies different didactic prototypes to structure courses in the Universidad Autónoma Metropolitana, campus Azcapotzalco, in Mexico City, project we have already presented in recent forums. Two different modes of application are implemented in classroom sessions and in structures workshop: the devices for functional demonstration of typical cases of structural work as well as the experimentation with student's own designs of destructible models where certain typologies are tested up to its failure limit. The first one allows teachers to explain adequately the theoretical principles and formulas (that usually are expressed on the blackboard) by means of didactic models identified in accordance to specific cases of the curriculum on variable level of complexity. This kind of practice allows the students of architecture and civil engineering to realize in better ways the possibilities of use and application of the different structural typologies. Such experimental models are part of more than fifty devices of the Laboratory's catalog. In the same sense, the possibility of observation of structural work of their own architectural designs, allows future professionals to achieve a better conception of the structural solutions that affect positively their designs. Based on specific predefined guides, the students develop their own architectural-structural projects and subject them to diverse loads, observing their behavior under the influence of variable stresses leading up the experiment to its last resistance. From both experiences a significant learning is obtained for the student's formation and training, who will be capable in his future professional work to use better tools of comprehension of the structural concepts applied to architecture as well as of increasing his conscience of the benefits and convenience of multidisciplinary work.Moreno, C.; Abad, A.; Gerdingh, JG.; Garcia M., C.; Gonzalez C., O. (2010). Didactic strategies for comprehension and learning of structural concepts. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/695