Effective governing equations for poroelastic growing media

A new mathematical model is developed for the macroscopic behaviour of a porous, linear elastic solid, saturated with a slowly flowing incompressible, viscous fluid, with surface accretion of the solid phase. The derivation uses a formal two-scale asymptotic expansion to exploit the well-separated length scales of the material: the pores are small compared to the macroscale, with a spatially periodic microstructure. Surface accretion occurs at the interface between the solid and fluid phases, resulting in growth of the solid phase through mass exchange from the fluid at a prescribed rate (and vice versa). The averaging derives a new poroelastic model, which reduces to the classical result of Burridge and Keller in the limit of no growth. The new model is of relevance to a large range of applications including packed snow, tissue growth, biofilms and subsurface rocks or soils

The role of Mechanics in Tumor growth : Modelling and Simulation

A number of biological phenomena are interlaced with classical mechanics. In this re- view are illustrated two examples from tumor growth, namely the formation of primordial networks of vessels (vasculogenesis) and the avascular phase of solid tumors. In both cases the formalism of con- tinuum mechanics, accompanied by accurate numerical simulations, are able to shed light on biological controversies. The converse is also true: non-standard mechanical problems suggest new challenging mathematical questions

Force traction microscopy: An inverse problem with pointwise observations

Force Traction Microscopy is an inversion method that allows to obtain the stress field applied by a living cell on the environment on the basis of a pointwise knowledge of the displacement produced by the cell itself. This classical biophysical problem, usually addressed in terms of Green functions, can be alternatively tackled using a variational framework and then a finite elements discretization. In such a case, a variation of the error functional under suitable regularization is operated in view of its minimization. This setting naturally suggests the introduction of a new equation, based on the adjoint operator of the elasticity problem. In this paper we illustrate the rigorous theory of the two-dimensional and three dimensional problem, involving in the former case a distributed control and in the latter case a surface control. The pointwise observations require to exploit the theory of elasticity extended to forcing terms that are Borel measure

Mass transport in morphogenetic processes: a second gradient theory for volumetric growth and material remodeling

International audienceIn this work, we derive a novel thermo-mechanical theory for growth and remodeling of biological materials in morphogenetic processes. This second gradient hyperelastic theory is the first attempt to describe both volumetric growth and mass transport phenomena in a single-phase continuum model, where both stress- and shape-dependent growth regulations can be investigated. The diffusion of biochemical species (e.g. morphogens, growth factors, migration signals) inside the material is driven by configurational forces, enforced in the balance equations and in the set of constitutive relations. Mass transport is found to depend both on first- and on second-order material connections, possibly withstanding a chemotactic behavior with respect to diffusing molecules. We find that the driving forces of mass diffusion can be written in terms of covariant material derivatives reflecting, in a purely geometrical manner, the presence of a (first-order) torsion and a (second-order) curvature. Thermodynamical arguments show that the Eshelby stress and hyperstress tensors drive the rearrangement of the first- and second-order material inhomogeneities, respectively. In particular, an evolution law is proposed for the first-order transplant, extending a well-known result for inelastic materials. Moreover, we define the first stress-driven evolution law of the second-order transplant in function of the completely material Eshelby hyperstress

a review of vasculogenesis models

Mechanical and chemical models of vasculogenesis are critically reviewed with an emphasis on their ability to predict experimentally measured quantities. Final remarks suggest a possibility to merge the capabilities of different models into a unified approach

Erratum to ?Cell directional persistence and chemotaxis in vascular morphogenesis? [Bull. Math. Biol. 66 (2004) 1851?1873]

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The dynamics of grouping-induced biases in apparent numerosity revealed by a continuous tracking technique

Connecting pairs of items causes robust underestimation of the numerosity of an ensemble, presumably by invoking grouping mechanisms. Here we asked whether this underestimation in numerosity judgments could be revealed and further explored by continuous tracking, a newly developed technique that allows for fast and efficient data acquisition and monitors the dynamics of the responses. Participants continuously reproduced the perceived numerosity of a cloud of dots by moving a cursor along a number line, while the number of dots and the proportion connected by lines varied over time following two independent random walks. The technique was robust and efficient, and correlated well with results obtained with a standard psychophysics task. Connecting objects with lines caused an underestimation of approximately 15% during tracking, agreeing with previous studies. The response to the lines was slower than the response to the physical numerosity, with a delay of approximately 150 ms, suggesting that this extra time is necessary for processing the grouping effect

Ideal observer analysis for continuous tracking experiments

Continuous tracking is a newly developed technique that allows fast and efficient data acquisition by asking participants to “track” a stimulus varying in some property (usually position in space). Tracking is a promising paradigm for the investigation of dynamic features of perception and could be particularly well suited for testing ecologically relevant situations difficult to study with classical psychophysical paradigms. The high rate of data collection may be useful in studies on clinical populations and children, who are unable to undergo long testing sessions. In this study, we designed tracking experiments with two novel stimulus features, numerosity and size, proving the feasibility of the technique outside standard object tracking. We went on to develop an ideal observer model that characterizes the results in terms of efficiency of conversion of stimulus strength into responses, and identification of early and late noise sources. Our ideal observer closely modeled results from human participants, providing a generalized framework for the interpretation of tracking data. The proposed model allows to use the tracking paradigm in various perceptual domains, and to study the divergence of human participants from ideal behavior