Adherent cells exert traction forces on to their environment which allows them to migrate, to maintain tissue integrity, and to form complex multicellular structures during developmental morphogenesis. Traction force microscopy (TFM) enables the measurement of traction forces on an elastic substrate and thereby provides quantitative information on cellular mechanics in a perturbation-free fashion. In TFM, traction is usually calculated via the solution of a linear system, which is complicated by undersampled input data, acquisition noise, and large condition numbers for some methods. Therefore, standard TFM algorithms either employ data filtering or regularization. However, these approaches require a manual selection of filter- or regularization parameters and consequently exhibit a substantial degree of subjectiveness. This shortcoming is particularly serious when cells in different conditions are to be compared because optimal noise suppression needs to be adapted for every situation, which invariably results in systematic errors. Here, we systematically test the performance of new methods from computer vision and Bayesian inference for solving the inverse problem in TFM. We compare two classical schemes, L1- and L2-regularization, with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization. Using artificial data and experimental data, we show that these methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Thus, Bayesian methods can mitigate the considerable uncertainty inherent in comparing cellular tractions in different conditions.

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PurposeTo investigate the dosimetric impact of point A definitions on both conventional point A plans and MRI-guided conformal high-dose-rate (HDR) brachytherapy plans.Material and methodsFifty-five HDR plans of 36 patients with FIGO stage I to IV cervical cancer were retrospectively studied; these included 30 conventional treatments and 25 conformal plans. Two different point A definitions were explored: the revised Manchester point A and the new point A as recommended by the American Brachytherapy Society. Conventional plans were produced by varying only the point A definition and the normalized isodose lines. Conformal plans were retrospectively generated per GEC-ESTRO recommendations based upon 3.0 Tesla MRI data.ResultsSmall yet significant variations were found in point A locations (mean: 0.5 cm, maximum: 2.1 cm, p < 0.001). The use of a new point A caused minimal dose variation for both conventional and conformal plans. Conventional plans normalized to the new point A generated up to 12% (avg. 1-3%) higher overall dose in terms of higher total reference air kerma than plans normalized to other points. Dosimetric changes due to point A definitions were up to 11-12% (avg. less than 2%) on target volumes or organs-at-risk.ConclusionsFor both conventional and conformal plans, the new point A definition leads to smaller variations caused during implant and/or differences in patient anatomy. Using the new point A is expected to produce more consistent brachytherapy plans and improve outcome analysis.

We review the construction and applications of exactly Poincaré invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincaré group on few-particle Hilbert spaces, the relation to quantum field theory, the formulation of cluster properties, and practical considerations related to the construction of realistic interactions and the solution of the dynamical equations. Selected applications illustrate the utility of this approach.