Imaging the In Vivo Degradation of Tissue Engineering Implants by Use of Supramolecular Radiopaque Biomaterials

For in situ tissue engineering (TE) applications it is important that implant degradation proceeds in concord with neo‐tissue formation to avoid graft failure. It will therefore be valuable to have an imaging contrast agent (CA) available that can report on the degrading implant. For this purpose, a biodegradable radiopaque biomaterial is presented, modularly composed of a bisurea chain‐extended polycaprolactone (PCL2000‐U4U) elastomer and a novel iodinated bisurea‐modified CA additive (I‐U4U). Supramolecular hydrogen bonding interactions between the components ensure their intimate mixing. Porous implant TE‐grafts are prepared by simply electrospinning a solution containing PCL2000‐U4U and I‐U4U. Rats receive an aortic interposition graft, either composed of only PCL2000‐U4U (control) or of PCL2000‐U4U and I‐U4U (test). The grafts are explanted for analysis at three time points over a 1‐month period. Computed tomography imaging of the test group implants prior to explantation shows a decrease in iodide volume and density over time. Explant analysis also indicates scaffold degradation. (Immuno)histochemistry shows comparable cellular contents and a similar neo‐tissue formation process for test and control group, demonstrating that the CA does not have apparent adverse effects. A supramolecular approach to create solid radiopaque biomaterials can therefore be used to noninvasively monitor the biodegradation of synthetic implants.     

Counterion, temperature, and time modulation of nanometric chiral ribbons from gemini-tartrate amphiphiles

Amphiphile supramolecular assemblies result from the cooperative effects of multiple weak interactions between a large number of subcomponents. As a result, prediction of and control over the morphologies of such assemblies remains difficult to achieve. Here, we described the fine-tuning of the shape, size, and morphology transitions of twisted and helical membranes formed by non-chiral dicationic n-2-n gemini amphiphiles complexed with chiral tartrate anions. We have reported that such systems express the chirality of the tartrate components at a supramolecular level and that the mechanism of the chiral induction by counterions involves specific anion cation recognition and the induction of conformationally labile chirality in the cations. Here, we demonstrate that the morphologies and dimensions of twisted and helical ribbons, as well as tubules, can be controlled and that interconversion between these structures can be induced upon modifying temperature, upon introducing small amounts of additives, or slightly modifying molecular structure. Specifically, electron microscopy, IR spectroscopy, and small-angle X-ray scattering show that (i) varying the hydrophobic chain length or adding gemini having bromide counterions (1%) or the opposite enantiomer (10%) leads to an increase of the diameter of membrane tubules from 33 to 48.5 nm; (ii) further addition (1.5%) of gemini bromide or a slight increase in temperature induces a transition from tubules to twisted ribbons; (iii) the twist pitch of the ribbons can be continuously tuned by varying enantiomeric excess; and (iv) it was also observed that the morphologies of these ribbons much evolve with time. Such unprecedented observations over easy tuning of the chiral supramolecular structures are clearly related to the original feature that the induction of chirality is solely due the counterions, which are much more mobile than the amphiphiles.     

Correction to: Estimating Measurement Uncertainty on Stress-Strain Curves from SHPB

Experimental Mechanics - A correction to this paper has been published: https://doi.org/10.1007/s11340-021-00702-z     

Asymptotic limit-cycle analysis of oscillating chemical reactions

The asymptotic limit-cycle analysis of mathematical models for oscillating chemical reactions is presented. In this work, after a brief presentation of mathematical preliminaries applied to the biased Van der Pol oscillator, we consider a two-dimensional model of the Chlorine dioxide Iodine Malonic-Acid (CIMA) reactions and the three-dimensional and two-dimensional Oregonator models of the Belousov–Zhabotinsky reactions. Explicit analytical expressions are given for the relaxation-oscillation periods of these chemical reactions that are accurate within 5% of their numerical values. In the two-dimensional CIMA and Oregonator models, we also derive critical parameter values leading to canard explosions and implosions in their associated limit cycles.

     

Dirac-bracket structure in multidimensional mode conversion

The intersection of two (2n − 1)-dimensional dispersion manifolds D_a and D_b in the 2n-dimensional ray phase space P yields a (2n − 2)-dimensional conversion manifold M≡D_a∩D_b that naturally possesses a Dirac-bracket structure that is inherited from the canonical Poisson bracket on ray phase space. The canonical symplectic two-form Ω ≡ Ω_∥ + Ω_⊥, defined on the 2n-dimensional tangent plane T_z0P≡T_z0M⊕(T_z0M)_⊥, can thus be decomposed into the Dirac two-form Ω_∥ on the (2n − 2)-dimensional tangent plane T_z0M at a conversion point z₀∈M, and the symplectic two-form Ω_⊥ on its orthogonal 2-dimensional complement (T_z0M)_⊥. These two symplectic two-forms are introduced in our analysis of multidimensional mode conversion, where their respective geometrical roles are defined. We note that since the Dirac-bracket structure Ω_∥ vanishes identically when n = 1, it represents a new structure in multidimensional (n > 1) mode conversion theory.