Computation of forces from deformed visco-elastic biological tissues. (26th February 2018)

• Record Type: Journal Article
• Authors: Muñoz, José J; Amat, David; Conte, Vito
• Is Part Of: Inverse problems. Volume 34:Number 4(2018:Apr.)
• Publication Date: 2018-02-26
• Subjects: viscoelasticity -- tractions -- tissue mechanics -- finite elements -- embryogenesis -- dipoles; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaac5b
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We present a least-squares based inverse analysis of visco-elastic biological tissues. The proposed method computes the set of contractile forces (dipoles) at the cell boundaries that induce the observed and quantified deformations. We show that the computation of these forces requires the regularisation of the problem functional for some load configurations that we study here. The functional measures the error of the dynamic problem being discretised in time with a second-order implicit time-stepping and in space with standard finite elements. We analyse the uniqueness of the inverse problem and estimate the regularisation parameter by means of an L-curved criterion. We apply the methodology to a simple toy problem and to an in vivo set of morphogenetic deformations of the Drosophila embryo.