Floppy modes and non-affine deformations in random fiber networks

We study the elasticity of random fiber networks. Starting from a microscopic picture of the non-affine deformation fields we calculate the macroscopic elastic moduli both in a scaling theory and a self-consistent effective medium theory. By relating non-affinity to the low-energy excitations of the network (``floppy-modes'') we achieve a detailed characterization of the non-affine deformations present in fibrous networks.Comment: 4 pages, 2 figures, new figure

Filamin cross-linked semiflexible networks: Fragility under strain

The semiflexible F-actin network of the cytoskeleton is cross-linked by a variety of proteins including filamin, which contain Ig-domains that unfold under applied tension. We examine a simple semiflexible network model cross-linked by such unfolding linkers that captures the main mechanical features of F-actin networks cross-linked by filamin proteins and show that under sufficiently high strain the network spontaneously self-organizes so that an appreciable fraction of the filamin cross-linkers are at the threshold of domain unfolding. We propose an explanation of this organization based on a mean-field model and suggest a qualitative experimental signature of this type of network reorganization under applied strain that may be observable in intracellular microrheology experiments of Crocker et al.Comment: 4 Pages, 3 figures, Revtex4, submitted to PR

Stiff Polymers, Foams and Fiber Networks

We study the elasticity of fibrous materials composed of generalized stiff polymers. It is shown that in contrast to cellular foam-like structures affine strain fields are generically unstable. Instead, a subtle interplay between the architecture of the network and the elastic properties of its building blocks leads to intriguing mechanical properties with intermediate asymptotic scaling regimes. We present exhaustive numerical studies based on a finite element method complemented by scaling arguments.Comment: 4 pages, 5 figure

Unfolding cross-linkers as rheology regulators in F-actin networks

We report on the nonlinear mechanical properties of a statistically homogeneous, isotropic semiflexible network cross-linked by polymers containing numerous small unfolding domains, such as the ubiquitous F-actin cross-linker Filamin. We show that the inclusion of such proteins has a dramatic effect on the large strain behavior of the network. Beyond a strain threshold, which depends on network density, the unfolding of protein domains leads to bulk shear softening. Past this critical strain, the network spontaneously organizes itself so that an appreciable fraction of the Filamin cross-linkers are at the threshold of domain unfolding. We discuss via a simple mean-field model the cause of this network organization and suggest that it may be the source of power-law relaxation observed in in vitro and in intracellular microrheology experiments. We present data which fully justifies our model for a simplified network architecture.Comment: 11 pages, 4 figures. to appear in Physical Review

Nonaffine rubber elasticity for stiff polymer networks

We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams stiff polymers easily deform in bending, while they are much stiffer with respect to tensile forces (``stretching''). Unlike in previous approaches, where network elasticity is derived from the stretching mode, our theory properly accounts for the soft bending response. A self-consistent effective medium approach is used to calculate the macroscopic elastic moduli starting from a microscopic characterization of the deformation field in terms of ``floppy modes'' -- low-energy bending excitations that retain a high degree of non-affinity. The length-scale characterizing the emergent non-affinity is given by the ``fiber length'' $l_f$, defined as the scale over which the polymers remain straight. The calculated scaling properties for the shear modulus are in excellent agreement with the results of recent simulations obtained in two-dimensional model networks. Furthermore, our theory can be applied to rationalize bulk rheological data in reconstituted actin networks.Comment: 12 pages, 10 figures, revised Section II

Porous structure of thick fiber webs

The bulk properties and stochastic pore geometry of finite-thickness fiber webs are studied using a realistic model for the sedimentation of flexible fibers [K. J. Niskanen and M. J. Alava, Phys. Rev. Lett. 73, 3475 (1994)]. The resulting web structure is controlled by a dimensionless number F=Tfwf/tf, where Tf is fiber flexibility, wf fiber width, and tf fiber thickness. The fiber length (≫wf,tf) is irrelevant. With increasing coverage c̄, a crossover occurs at c̄=c0≈1+2F from a vacancy-controlled two-dimensional (2D) structure to a pore-controlled 3D structure. The 3D structures are isomorphic in that the pore dimensions are exponentially distributed, with the decay rate dependent only on F.Peer reviewe

Mechanical properties of nanotube sheets: Alterations in joint morphology and achievable moduli in manufacturable materials

Nanotube sheets, or “bucky papers,” have been proposed for use in actuating, structural and electrochemical systems, based in part on their potential mechanical properties. Here, we present results of detailed simulations of networks of nanotubes/ropes, with special emphasis on the effect of joint morphology. We perform detailed simulations of three-dimensional joint deformation, and use the results to inform simulations of two-dimensional (2D) networks with intertube connections represented by torsion springs. Upper bounds are established on moduli of nanotube sheets, using the 2D Euler beam-network simulations. Comparisons of experimental and simulated response for HiPco-nanotube and laser-ablated nanotube sheets, indicate that ∼2–30-fold increases in moduli may be achievable in these materials. Increasing the numbers of interrope connections appears to be the best target for improving nanotube sheet stiffnesses in materials containing straight segments. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70283/2/JAPIAU-95-8-4335-1.pd

Kypho-IORT - a novel approach of intraoperative radiotherapy during kyphoplasty for vertebral metastases

<p>Abstract</p> <p>Background</p> <p>Instable and painful vertebral metastases in patients with progressive visceral metastases present a common therapeutic dilemma. We developed a novel approach to deliver intraoperative radiotherapy (IORT) during kyphoplasty and report the first treated case.</p> <p>Methods/Results</p> <p>60 year old patient with metastasizing breast cancer under chemotherapy presented with a newly diagnosed painful metastasis in the 12^ththoracic vertebra. Under general anaesthesia, a bipedicular approach into the vertebra was chosen with insertion of specially designed metallic sleeves to guide the electron drift tube of the miniature X-ray generator (INTRABEAM, Carl Zeiss Surgical, Oberkochen, Germany). This was inserted with a novel sheet designed for this approach protecting the drift tube. A radiation dose of 8 Gy in 5 mm distance (50 kV X-rays) was delivered. The kyphoplasty balloons (KyphX, Kyphon Inc, Sunnyvale) were inflated after IORT and polymethylmethacrylate cement was injected. The whole procedure lasted less than 90 minutes.</p> <p>Conclusion</p> <p>In conclusion, this novel, minimally invasive procedure can be performed in standard operating rooms and may become a valuable option for patients with vertebral metastases providing immediate stability and local control. A phase I/II study is under way to establish the optimal dose prescription.</p