L1-regularized reconstruction for traction force microscopy

Proceeding of: 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI). IEEE, Prague, 13-16 April, 2016.Traction Force Microscopy (TFM) is a technique widely used to recover cellular tractions from the deformation they cause in their surrounding substrate. Traction recovery is an ill-posed inverse problem that benefits of a regularization scheme constraining the solution. Typically, Tikhonov regularization is used but it is well known that L1-regularization is a superior alternative to solve this type of problems. For that, recent approaches have started to explore what could be their contribution to increase the sensitivity and resolution in the estimation of the exerted tractions. In this manuscript, we adapt the L1-regularization of the curl and divergence to 2D TFM and compare the recovered tractions on simulated and real data with those obtained using Tikhonov and L1-norm regularization.This work was partially supported by the European Research Council (ERC) under the EU-FP7/2007-2013 through ERC Grant Agreement nº 308223, and the Spanish Ministry of Economy and Competitiveness (TEC2013-48552-C2-1-R). European Community's Seventh Framework ProgramEuropean Community's Seventh Framework Progra

Full L-1-regularized Traction Force Microscopy over whole cells

Background Traction Force Microscopy (TFM) is a widespread technique to estimate the tractions that cells exert on the surrounding substrate. To recover the tractions, it is necessary to solve an inverse problem, which is ill-posed and needs regularization to make the solution stable. The typical regularization scheme is given by the minimization of a cost functional, which is divided in two terms: the error present in the data or data fidelity term; and the regularization or penalty term. The classical approach is to use zero-order Tikhonov or L2-regularization, which uses the L2-norm for both terms in the cost function. Recently, some studies have demonstrated an improved performance using L1-regularization (L1-norm in the penalty term) related to an increase in the spatial resolution and sensitivity of the recovered traction field. In this manuscript, we present a comparison between the previous two regularization schemes (relying in the L2-norm for the data fidelity term) and the full L1-regularization (using the L1-norm for both terms in the cost function) for synthetic and real data. Results Our results reveal that L1-regularizations give an improved spatial resolution (more important for full L1-regularization) and a reduction in the background noise with respect to the classical zero-order Tikhonov regularization. In addition, we present an approximation, which makes feasible the recovery of cellular tractions over whole cells on typical full-size microscope images when working in the spatial domain. Conclusions The proposed full L1-regularization improves the sensitivity to recover small stress footprints. Moreover, the proposed method has been validated to work on full-field microscopy images of real cells, what certainly demonstrates it is a promising tool for biological applications.This work was partially supported by the Spanish Ministry of Economy and Competitiveness (TEC2013-48552-C2-1-R, TEC2015-73064-EXP and TEC2016-78052-R) (AMB, ASA) and (SAF2014-54705-R) (MVM, RAC), the European Research Council (ERC) under the EU-FP7/2007-2013 through ERC Grant Agreement n° 308,223 (HVO, AJP). ASA is supported by an FPI grant of the Spanish Ministry of Economy and Competitiveness. MVM is supported by a Marie Curie Grant (CIG293719) and a Ramon y Cajal fellowship (RYC2010-06094) from the Spanish Ministry of Economy and Competitiveness

Free Form Deformation-Based Image Registration Improves Accuracy of Traction Force Microscopy

Traction Force Microscopy (TFM) is a widespread method used to recover cellular tractions from the deformation that they cause in their surrounding substrate. Particle Image Velocimetry (PIV) is commonly used to quantify the substrate's deformations, due to its simplicity and efficiency. However, PIV relies on a block-matching scheme that easily underestimates the deformations. This is especially relevant in the case of large, locally non-uniform deformations as those usually found in the vicinity of a cell's adhesions to the substrate. To overcome these limitations, we formulate the calculation of the deformation of the substrate in TFM as a non-rigid image registration process that warps the image of the unstressed material to match the image of the stressed one. In particular, we propose to use a B-spline -based Free Form Deformation (FFD) algorithm that uses a connected deformable mesh to model a wide range of flexible deformations caused by cellular tractions. Our FFD approach is validated in 3D fields using synthetic (simulated) data as well as with experimental data obtained using isolated endothelial cells lying on a deformable, polyacrylamide substrate. Our results show that FFD outperforms PIV providing a deformation field that allows a better recovery of the magnitude and orientation of tractions. Together, these results demonstrate the added value of the FFD algorithm for improving the accuracy of traction recovery.Funded by Ministerio de Economía y Competividad (ES); url: http://www.mineco.gob.es/; RyC2010-06094, Fundación Ramón Areces (ES); url: http://www.fundacionareces.es/fundacionareces/, Ministerío de Economía y Competividad (ES); url: http://www.mineco.gob.es/; SAF2011-24953 (MVM); Ministerio de Economía y Competividad (ES); url: http://www.mineco.gob.es/; DPI2012-38090-C1, European Research Council (BE); url: http://erc.europa.eu/; 306751 (JMGA); European Research Council (BE); url: http://erc.europa.eu/; 308223 (HVO); Ministerio de Economía y Competividad (ES); url: http://www.mineco.gob.es/; DPI2012-38090-C3 (COS); and Ministerio de Economía y Competividad (ES); url: http://www.mineco.gob.es/; TEC2013- 48552-C2-1-R (AMB). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.European Community's Seventh Framework Progra

Clonal chromosomal mosaicism and loss of chromosome Y in elderly men increase vulnerability for SARS-CoV-2

The pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, COVID-19) had an estimated overall case fatality ratio of 1.38% (pre-vaccination), being 53% higher in males and increasing exponentially with age. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, we found 133 cases (1.42%) with detectable clonal mosaicism for chromosome alterations (mCA) and 226 males (5.08%) with acquired loss of chromosome Y (LOY). Individuals with clonal mosaic events (mCA and/or LOY) showed a 54% increase in the risk of COVID-19 lethality. LOY is associated with transcriptomic biomarkers of immune dysfunction, pro-coagulation activity and cardiovascular risk. Interferon-induced genes involved in the initial immune response to SARS-CoV-2 are also down-regulated in LOY. Thus, mCA and LOY underlie at least part of the sex-biased severity and mortality of COVID-19 in aging patients. Given its potential therapeutic and prognostic relevance, evaluation of clonal mosaicism should be implemented as biomarker of COVID-19 severity in elderly people. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, individuals with clonal mosaic events (clonal mosaicism for chromosome alterations and/or loss of chromosome Y) showed an increased risk of COVID-19 lethality

L1-Regularized Reconstruction for Traction Force Microscopy

Traction Force Microscopy (TFM) is a technique widely used to recover cellular tractions from the deformation they cause in their surrounding substrate. Traction recovery is an ill-posed inverse problem that benefits of a regularization scheme constraining the solution. Typically, Tikhonov regularization is used but it is well known that L1- regularization is a superior alternative to solve this type of problems. For that, recent approaches have started to explore what could be their contribution to increase the sensitivity and resolution in the estimation of the exerted tractions. In this manuscript, we adapt the L1-regularization of the curl and divergence to 2D TFM and compare the recovered tractions on simulated and real data with those obtained using Tikhonov and L1-norm regularization.status: publishe

Super-resolved Traction Force Microscopy over Whole Cells

Traction Force Microscopy (TFM) is a commonly used technique to compute cellular tractions that cells exert to the surrounding substrate. Traction recovery is an ill-posed inverse problem, which needs regularization to stabilize the solution. Due to its simplicity, Tikhonov or L2-regularization is usually used, but recent studies have demonstrated the increase of sensitivity and resolution in the recovered tractions using an L1-regularization scheme. In this manuscript, we present an approximation that makes feasible the traction recovery on full-size microscope images when working in the spatial domain. We perform also a comparison between the two regularization schemes named before (relying in L2-norm for the data fidelity term) and the full L1-regularization (using L1-norm for both the regularization and data fidelity terms). Our proof-of concept using real data reveal that L1-regularizations might give an improved resolution (more accused for full L1-regularization) and a reduction in the background noise with respect to the classical zero-order Tikhonov regularization.status: publishe

Three-dimensional rapid visualisation of matrix deformations around angiogenic sprouts

status: publishe

Quantification of 3D Matrix Deformations induced by Angiogenic Sprouts in Fibrillar Gels

Cell-matrix mechanical interactions play a key role in a variety of physiological processes. Recently, the quantification of cellular tractions by means of traction force microscopy has been extended to 3D cell cultures. However, typically assumed simplifications during the mechanical characterization of the matrix could affect the retrieved traction magnitudes. On the other hand, cell induced matrix displacements already provide quantitative information on cell-matrix mechanical interaction, avoiding the complexity inherent to traction reconstruction. In this study, we assess the deformations induced by angiogenic cellular sprouts in a fibrillar matrix under chemically defined culture conditions from the full field displacements obtained with and without fluorescent beads acting as fiducial markers. Human umbilical vein endothelial cells (HUVEC) were seeded on top of a collagen gel and induced with pro-angiogenic factors to form multicellular sprouts. The sprouts were grown in endothelial cell growth medium (EGM2) supplemented with or without blebbistatin or cytochalasin D. As control for the calculation of the matrix deformations, 200 nm fluorescent beads were attached to the collagen fibers. Second harmonic generation (SHG) and laser-scanning confocal microscopy were used to acquire Z-stacks of label-free collagen fibers and fluorescent beads, respectively, during the live imaging before and after chemically induced relaxation of cells. The calculation of the matrix deformations was formulated as a B-spline –based 3D non-rigid image registration process that warps the image of the stressed gel to match the image of the gel after relaxation [1]. The calculation of these displacements was independently performed from fiber (without fiducial markers) and bead images. We observed that the recovered displacements (Figure 1) from the label-free fiber images were equivalent to the ones obtained from bead images, showing magnitudes ranging between 1 to 8 µm before the blocking effects of blebbistatin or cytochalasin D on acto-myosin force generation. Our methodology allows mapping cell-induced 3D matrix deformations around multicellular sprouts embedded in fibrillar gels without the need for fluorescent beads, which could alter the matrix mechanical properties. The resulting information is expected to provide a quantitative view of the cell-matrix mechanical interaction of HUVECs in 3D and leads to a better comprehension of cell mechanobiology in sprouting angiogenesis.status: accepte

Efficient Recovery of 3D Forces exerted by Cells on Thin Substrates

status: accepte

Spatiotemporal analyses of cellular tractions characterize the effect of substrate stiffness and adhesion molecule at subcellular scale

Poster presentationstatus: accepte