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Morphogenesis

Authors: G.B. Blanchard, A.J. Kabla, N.L. Schultz, L.C. Butler, B. Sanson, N. Gorfinkiel, L. Mahadevan and R.J. Adams

Nature Methods, 6, 458-464 (2009), DOI:10.1038/NMETH.1327.

The dynamic reshaping of tissues during morphogenesis results from a combination of individual cell behaviors and collective cell rearrangements. However, a comprehensive framework to unambiguously measure and link cell behavior to tissue morphogenesis is lacking. Here we introduce such a kinematic framework, bridging cell and tissue behaviors at an intermediate, mesoscopic, level of cell clusters or domains. By measuring domain deformation in terms of the relative motion of cell positions and the evolution of their shapes, we characterized the basic invariant quantities that measure fundamental classes of cell behavior, namely tensorial rates of cell shape change and cell intercalation. In doing so we introduce an explicit definition of cell intercalation as a continuous process. We mapped strain rates spatiotemporally in three models of tissue morphogenesis, gaining insight into morphogenetic mechanisms. Our quantitative approach has broad relevance for the precise characterization and comparison of morphogenetic phenotypes.

Cell shape changes indicate a role for extrinsic tensile forces in Drosophila germ-band extension

Authors: L.C. Butler, G.B. Blanchard, A.J. Kabla, N.J. Lawrence, D.P. Welchman, L. Mahadevan, R.J. Adams and B. Sanson

Nature Cell biology, 2009 DOI:10.1038/ncb1894.

Drosophila germ-band extension (GBE) is an example of the convergence and extension movements that elongate and narrow embryonic tissues. To understand the collective cell behaviours underlying tissue morphogenesis, we have continuously quantified cell intercalation and cell shape change during GBE. We show that the fast, early phase of GBE depends on cell shape change in addition to cell intercalation. In antero-posterior patterning mutants such as those for the gap gene Krüppel, defective polarized cell intercalation is compensated for by an increase in antero-posterior cell elongation, such that the initial rate of extension remains the same. Spatio-temporal patterns of cell behaviours indicate that an antero-posterior tensile force deforms the germ band, causing the cells to change shape passively. The rate of antero-posterior cell elongation is reduced in twist mutant embryos, which lack mesoderm. We propose that cell shape change contributing to germ-band extension is a passive response to mechanical forces caused by the invaginating mesoderm.

Mechanical networks & biogels

Strain-induced alignment in collagen gels

Authors: David Vader, Alexandre Kabla, David Weitz, L. Mahadevan

PLoS ONE 4(6): e5902. doi:10.1371/journal.pone.0005902.

Collagen is the most abundant extra-cellular-network-forming protein in animal biology and is important in both natural and artificial tissues where it serves as a material of great mechanical versatility. Much of this versatility arises from its almost unique ability to remodel under applied loads into anisotropic and inhomogeneous structures. We explore the origins of this versatility by probing the mechanical response of fibrous collagenous networks in a load cell that mimics the typical deformation profile imposed by cells in vivo. We observe strong fiber alignment and densification as a function of applied strain for both uncrosslinked and crosslinked networks. This alignment is found to be irreversibly imprinted in uncrosslinked collagen networks, and suggests a simple mechanism for tissue organization at the microscale. However, this behaviour becomes reversible when the fiber binding strength is increased by addition of a crosslinker, indicating that these effects are primarily elastic, and part of the fundamental non-linear properties of fibrous biological networks.

Elasticity  of floppy and stiff random networks

Authors: M. Wyart, H. Liang, A. Kabla and L. Mahadevan

Phys.Rev.Lett. 101:215501 (2008).

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network dz; a floppy network has dz < 0, while a stiff network has dz > 0. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of nonaffine displacements, and the network stiffening as a function of dz, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.

Nonlinear mechanics of soft fibre networks

Authors: Alexandre Kabla, L. Mahadevan

J. R. Soc. Interface, 4(12) 99-106 (2007)
PubMed: 17015287

Mechanical networks of fibres arise on a range of scales in nature and technology, from the cytoskeleton of a cell to blood clots, from textiles and felts to skin and collageneous tissues. Their collective response is dependent on the individual response of the constituent filaments as well as the density and topology and order in the network. Here we use the example of a low density synthetic felt of athermal filaments to study the generic features of the mechanical response of such networks including strain stiffening and negative normal stress effects. A simple microscopic model allows us to explain these features of our observations, and provides us with a baseline framework to understand active biomechanical networks.

Foam Rheology

Quasistatic rheology of foams - I. Oscillating strain

Authors: Alexandre Kabla, Georges Debregeas

Quasistatic rheology of foams - II. Continuous shear flow

Authors: Alexandre Kabla, Julien Scheibert, Georges Debregeas

Journal of Fluid Mechanics, Volume 587 (2007), pages  45-72.

The evolution of a bidimensional foam submitted to continuous quasistatic shearing is investigated both experimentally and numerically. We extract, from the images of the sheared foam, the plastic flow profiles as well as the local statistical properties of the stress field. When the imposed strain becomes larger than the yield strain, the plastic events develop large spatial and temporal correlations, and the plastic flow gets confined to a narrow shear-band. This transition and the steady-state regime of flow are investigated by first focusing on the elastic deformation produced by an elementary plastic event. This allows us to understand (1) the appearance of long-lived spatial heterogeneities of the stress field, which we believe are at the origin of the shear-banding transition, (2) the statistics of the dynamic fluctuations of the stress field induced by plastic rearrangements in steady-state regime.

Local stress relaxation and shear-banding in a dry foam under shear

Authors: Alexandre Kabla, Georges Debregeas

Physical Review Letters, 90 (25), 258303 (2003)

We have developed a realistic simulation of 2D dry foams under quasi-static shear. After a short transient, a shear-banding instability is observed with flow characteristics very similar to measurements obtained on real foams. This numerical model allows us to probe the mechanical response of the material to a single plastication event. From the analysis of this elastic propagator, we propose a scenario for the onset and stability of the flow localization process in foams, which should remain valid for most athermal amorphous systems under creep flow.

Granular Matter / Matériaux granulaires

Dilatancy in Slow Granular Flows

Authors: Alexandre Kabla, Tim Senden

Physical Review Letters, 102, 228301 (200)

When walking on wet sand, each footstep leaves behind a temporarily dry impression. This counter intuitive observation is the most common illustration of the Reynolds principle of dilatancy: that is, a granular packing tends to expand as it is deformed. As a consequence, the amount of porous space increases, resulting in the apparent drying of the footprint. Although widely called upon in areas such as soil mechanics, geomechanics, as well as many industrial processes, a deeper understanding of this principle is constrained by the lack of analytical techniques to study this behaviour. Using X-ray radiography we track a broad variety of granular flow profiles and quantify their intrinsic dilatancy behaviour. These measurements frame Reynolds dilatancy as a kinematic process. Closer inspection demonstrates however the practical importance of flow induced compaction which competes with dilatancy, leading more complex flow properties than expected.

X-ray observation of micro-failures in granular piles approaching an avalanche

Authors: Alexandre Kabla, Georges Debregeas, Jean-Marc Di Meglio, Tim Senden

EuroPhysics Letter 71:932 (2005)

An X-ray imaging technique is used to probe the stability of 3-dimensional granular packs in a slowly rotating drum. Well before the surface reaches the avalanche angle, we observe intermittent plastic events associated with collective rearrangements of the grains located in the vicinity of the free surface. The energy released by these discrete events grows as the system approaches the avalanche threshold. By testing various preparation methods, we show that the pre-avalanche dynamics is not solely controlled by the difference between the free surface inclination and the avalanche angle. As a consequence, the measure of the pre-avalanche dynamics is unlikely to serve as a tool for predicting macroscopic avalanches.

The geometry and the number of contacts of monodisperse sphere packs using X-ray tomography

Authors: M. Saadarfar, A. Kabla, T.J. Senden et T. Aste,

Powders and Grains 2005 R. Garcia-Rojo, H.J. Hermann and S. McNamara, Eds., Volume I, 2005, A.A. Balkema Publishers, London, ISBN 0 415 38348 X, pp. 33-36

Contact dynamics in a gently vibrated granular pile

Authors: Alexandre Kabla, Georges Debregeas

Physical Review Letters, 92 (3), 035501 (2004)

We use multi-speckle diffusive wave spectroscopy (MSDWS) to probe the micron-scale dynamics of a granular pile submitted to discrete gentle taps. The typical time-scale between plastic events is found to increase dramatically with the number of applied taps. Furthermore, this microscopic dynamics weakly depends on the solid fraction of the sample. This process is strongly analogous to the aging phenomenon observed in thermal glassy systems. We propose a heuristic model where this slowing down mechanism is associated with a slow evolution of the distribution of the contact forces between particles. This model accounts for the main features of the observed dynamics.

Medical imaging

Real-Time Tracking and Shape Segmentation of Atrial Septal Defects in 3D echocardiography

Authors: M. G. Linguraru , A. Kabla , G. R. Marx , P. J. del Nido , R. D. Howe

Academic Radiology 14:1298 (2007)

Real-time cardiac ultrasound allows monitoring the heart motion during intracardiac beating heart procedures. Our application assists atrial septal defect (ASD) closure techniques using real-time 3D ultrasound guidance. One major image processing challenge is the low image quality, especially given the required processing of information at high frame rate. We present an optimized block flow technique, which combines the probability-based velocity computation for an entire block with cyclic template matching. We propose adapted similarity constraints both from frame to frame to conserve energy, and globally from a reference template to minimize errors. Computing velocity at the block level with an optimized scheme, our technique tracks ASD motion at a frequency of 60 frames/s on clinical 4D datasets. ASD tracking is also an important tool towards systematic clinical studies of the dynamic behavior of the intra-atrial communication. In particular, we show real-time tracking and preliminary segmentation results of the ASD shape and orientation as a function of time.

Real-Time Block Flow Tracking of Atrial Septal Defect Motion in 4D Cardiac Ultrasound

Authors: M. G. Linguraru , A. Kabla , N. V. Vasilyev , P. J. del Nido , R. D. Howe

2007 IEEE International Symposium on Biomedical Imaging. Proceedings. p. 356-359.