Surface response of a viscoelastic medium to subsurface acoustic sources with application to medical diagnosis

The response at the surface of an isotropic viscoelastic medium to buried fundamental acoustic sources is studied theoretically, computationally and experimentally. Finite and infinitesimal monopole and dipole sources within the low audible frequency range (40-400 Hz) are considered. Analytical and numerical integral solutions that account for compression, shear and surface wave response to the buried sources are formulated and compared with numerical finite element simulations and experimental studies on finite dimension phantom models. It is found that at low audible frequencies, compression and shear wave propagation from point sources can both be significant, with shear wave effects becoming less significant as frequency increases. Additionally, it is shown that simple closed-form analytical approximations based on an infinite medium model agree well with numerically obtained "exact" half-space solutions for the frequency range and material of interest in this study. The focus here is on developing a better understanding of how biological soft tissue affects the transmission of vibro-acoustic energy from biological acoustic sources below the skin surface, whose typical spectral content is in the low audible frequency range. Examples include sound radiated from pulmonary, gastro-intestinal and cardiovascular system functions, such as breath sounds, bowel sounds and vascular bruits, respectively.     

On the solutions of the linear integral equations of Volterra type

Some boundaries about the solution of the linear Volterra integral equations of the form f(t)=1?K*f were obtained as |f(t)|?1, |f(t)|?2 and |f(t)|?4 in (J. Math. Anal. Appl. 1978; 64 :381–397; Int. J. Math. Math. Sci. 1982; 5 (1):123–131). The boundary of the solution function of an equation in this type was found as |f(t)|?2ⁿ in (Integr. Equ. Oper. Theory 2002; 43 :466–479), where t∈[0, ∞) and n is a natural number such that n?2. In (Math. Comp. 2006; 75 :1175–1199), it is shown that the boundary of the solution function of an equation in the same form can also be derived as that of (Integr. Equ. Oper. Theory 2002; 43 :466–479) under different conditions than those of (Integr. Equ. Oper. Theory 2002; 43 :466–479). In the present paper, the sufficient conditions for the boundedness of functions f, f′, f′′, …, f⁽ⁿ⁺³⁾, (n∈?) defined on the infinite interval [0, ∞) are given by our method, where f is the solution of the equation f(t)=1?K*f. Copyright © 2007 John Wiley & Sons, Ltd.     

Expansion of the boundaries of the solutions of the linear Volterra integral equations with convolution kernel

We solve a certain differential equation and system of integral equations. As applications, we characterize holomorphic symbols of commuting Toeplitz operators on the pluriharmonic Bergman space. In addition, pluriharmonic symbols of normal Toeplitz operators are characterized. Also, zero semi-commutators for certain classes of Toeplitz operators are characterized.This research is partially supported by KOSEF(98-0701-03-01-5).     

Carotenoids and Related Compounds. Part 36.. Further syntheses of zeaxanthin and rhodoxanthin

A modification of a previously reported synthesis of zeaxanthin ( 1 ), and routes to both zeaxanthin and rhodoxanthin ( 2 ) from α-ionone, are described.     

Mechanisms of nucleophilic substitution reactions of methylated hydroxylamines with bis(2,4-dinitrophenyl)phosphate. Mass spectrometric identification of key intermediates

Mono- and dimethylation of hydroxylamine on nitrogen does not significantly affect rates of initial attack of NHMeOH and NMe(2)OH on bis(2,4-dinitrophenyl)phosphate (BDNPP), which is largely by oxygen phosphorylation. O-Methylation, however, blocks this reaction and NH(2)OMe then slowly reacts with BDNPP via N-attack at phosphorus and at the aryl group. With NHMeOH, the initial product of O-attack at phosphorus reacts further, either by reaction with a second NHMeOH or by a spontaneous shift of NHMe to the aryl group via a transient cyclic intermediate. There is a minor N-attack of NHMeOH on BDNPP in an S(N)2(Ar) reaction. Reactions occurring via N-attack are blocked by N-dimethylation, and reaction of NMe(2)OH with BDNPP occurs via O-attack, generating a long-lived product. Reaction mechanisms have been probed, and intermediates identified, by using both NMR and MS spectroscopy, with the novel interception of key reaction intermediates in the course of reaction by electrospray ionization mass and tandem mass spectrometry.     

The effects of chronic hypoperfusion on rat cranial bone mineral and organic matrix

Arteriovenous malformations (AVM) of the brain, errors in the development of the vasculature, produce high flow arteriovenous shunts. They steal blood from surrounding brain tissue, which is chronically hypoperfused. Hypoperfusion is a condition of inadequate tissue perfusion and oxygenation resulting in abnormal tissue metabolism. In the present study Fourier transform infrared (FTIR) spectroscopy was used to investigate the effects of hypoperfusion on rat cranial bone mineral and organic matrix at the molecular level. FTIR spectroscopic analysis revealed that in cranial bones of an experimental group the relative amount of carbonate and phosphate groups increased whereas that of protein (amide I) decreased. Curve-fitting analysis of the v₂ carbonate band showed that amounts of type A and type B carbonates increased slightly (p=0.423 for both) whereas, type L carbonate decreased slightly (p=0.522) in hypoperfused cranial bones. Analysis of the C–H region revealed a significant increase (p=0.037) in the lipid to protein ratio. Because the lipid content is high, hypoperfused cranial bone tissue is more prone to lipid peroxidation. Dialdehydes derived from lipid peroxidation can make cross-links with collagen and might lead to disturbances in the collagen cross-link profile. The 1660 cm^–1/1690 cm^–1 partial area ratio derived from curve-fitting analysis of the Amide I band is sensitive to the relative amount of collagen non-reducible cross-link hydroxylysyl/lysylpyridinolines (Pyr) and reducible cross-link dihydroxylysinonorleucine (DHLNL) and this ratio reflects collagen maturity. In chronic hypoperfusion a significant decrease (p=0.004) was observed in this ratio. This means there were less mature collagen cross-links. Disturbances in the collagen maturation can affect mineralization process and lead to formation of pathologic structures in cranial bones. These findings clearly demonstrate that FTIR spectroscopy can be used to extract valuable information at molecular level, leading to better understanding of the effect of hypoperfusion on rat cranial bones.     

Dynamic analysis of beams on viscoelastic foundation

This study is intended to analyze dynamic behavior of beams on Pasternak-type viscoelastic foundation subjected to time-dependent loads. The Timoshenko beam theory is adopted in the derivation of the governing equation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate exactly the dynamic stiffness matrix of the problem. The solutions obtained are transformed to the real space using the Durbin's numerical inverse Laplace transform method. The dynamic response of beams on viscoelastic foundation is analyzed through various examples.     

Dendron–polymer conjugates via the diels–alder “click” reaction of novel anthracene‐based dendrons

Diblock and triblock dendron–polymer conjugates containing biodegradable polyester dendron blocks and polyethylene glycol (PEG) polymer were synthesized using the Diels–Alder “click” cycloaddition reaction. PEG polymers with furan‐protected maleimide functionality were synthesized and reacted with biodegradable polyester dendrons containing an anthracene moiety at their focal point. First through third generations of biodegradable polyester dendrons containing an anthracene unit at their focal point were synthesized using a divergent strategy. Efficient conjugation of the dendrons to polymers was demonstrated using ¹HNMR and size exclusion chromatography. This modular approach provides an easy access to the design of multivalent PEG conjugates. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3191–3201     

Synthesis of pyrene end‐capped A6 dendrimer and star polymer with phosphazene core via “click chemistry”

Novel hexa‐armed and pyrene (Pyr) end‐capped phosphazene dendrimer [N₃P₃‐(Pyr)₆] and star polymer with poly(ε‐caprolactone) (PCL) arms [N₃P₃‐(PCL‐Pyr)₆] were prepared via two series of reactions. In these series, core‐first approach was used starting from a hexa‐hydroxy functional phosphazene derivative (N₃P₃‐(OH)₆). It was used as an initiator in the ring‐opening polymerization of ε‐caprolactone to prepare a hexa‐armed PCL star polymer (N₃P₃‐(PCL‐OH)₆). Hydroxyl functionalities of N₃P₃‐(OH)₆ and N₃P₃‐(PCL‐OH)₆ were then successfully converted into bromide and azide, in turn. Further end‐group modifications of azide functional dendrimer precursor (N₃P₃‐(N₃)₆) and star polymer (N₃P₃‐(PCL‐N₃)₆) were achieved quantitatively via the Cu(I) catalyzed click reaction between azide functional groups and 1‐ethynyl pyrene in the final step. Moreover, the pyrene end‐capped phosphazene dendrimer and star polymer were used in noncovalent functionalization of multiwalled carbon nanotubes. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011