Triadic Functions Research Articles

Precis of Conjoining Meanings

Precis of Conjoining Meanings

TGF-β: the sword, the wand, and the shield of FOXP3+ regulatory T cells

Since its rediscovery in the mid-1990s, FOXP3(+) regulatory T cells (Tregs) have climbed the rank to become commander-in-chief of the immune system. They possess diverse power and ability to orchestrate the immune system in time of inflammation and infection as well as in time of harmony and homeostasis. To be the commander-in-chief, they must be equipped with both offensive and defensive weaponry. This review will focus on the function of transforming growth factor-β (TGF-β) as the sword, the wand, and the shield of Tregs. Functioning as a sword, this review will begin with a discussion of the evidence that supports how Tregs utilize TGF-β to paralyze cell activation and differentiation to suppress immune response. It will next provide evidence on how TGF-β from Tregs acts as a wand to convert naïve T cells into iTregs and Th17 to aid in their combat against inflammation and infection. Lastly, the review will present evidence on the role of TGF-β produced by Tregs in providing a shield to protect and maintain Tregs against apoptosis and destabilization when surrounded by inflammation and constant stimulation. This triadic function of TGF-β empowers Tregs with the responsibility and burden to maintain homeostasis, promote immune tolerance, and regulate host defense against foreign pathogens.

Kirchhoff evaluation of scattered elastic wavefields in anisotropic media

Three-dimensional elastic wave scattering is addressed for the case of general anisotropic materials. For traction-free scatterers the elastodynamic Kirchhoff approximation is applied, which is valid at high frequencies and near specular angles. Based on a mathematical formulation including Green’s triadic stress tensor function, asymptotic evaluation yields the displacement vector of the scattered wavefield in a form which is convenient for effective numerical computation. The (point source) far-field approximation applied to Green’s triadic function is valid in noncaustic regions.

Elastic wave propagation in transversely isotropic media. II. The generalized Rayleigh function and an integral representation for the transducer field. Theory

The basis for the derivation of elastodynamic holography for arbitrarily oriented transversely isotropic materials, given in Part I of this presentation [M. Spies, J. Acoust. Soc. Am. 96, 1144–1157 (1994)], is Huygens’ principle and a resulting relationship which links the spatial spectra of surface traction and displacement distribution. Similar to deriving the plane-wave spectral decomposition of elastic wavefields for given displacement, this relationship yields a corresponding decomposition for the case of given surface traction, which can be applied to model the problem of transducer radiation as significant to nondestructive testing. For a physically reasonable distribution of surface traction within the transducer aperture, an integral representation for the resulting transducer field is obtained. The main problem in this approach is the inversion of the 2-D space-time spectral representation of Green’s triadic function. A specifically interesting result of this inversion is the Rayleigh function for arbitrarily oriented transversely isotropic media, which characterizes the propagation of the respective Rayleigh wavefronts. Since the resulting expressions are explicitly dependent on the orientation of the material’s axis of rotational symmetry, their numerical evaluation will be much more complicated than in the isotropic case.