Linear, weakly nonlinear and fully nonlinear models for soft tissues: which ones provide the most reliable estimations of the stiffness?

Benign and malignant lesions in tissues or organs can be detected by elastographic investigations in which pathological regions are spotted from local alterations of the stiffness. As is known, the shear modulus provides a measure of the stiffness of an elastic material. Based on the classical theory of linear elasticity, an elastogram yields estimations of the linear shear modulus from measurements of the speed of small-amplitude transverse waves propagating in the medium tested. In this paper, we show that the estimation of the shear modulus can be improved significantly by employing the fourth-order weakly nonlinear theory of elasticity (FOE), and indicate how the stiffness can be assessed more precisely with the use of FOE. We discuss also why FOE provides more reliable results than the fully nonlinear theory of elasticity. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Determination of pyrethroid pesticide residues in fatty materials by solid-matrix dispersion partition, followed by mini-column size-exclusion chromatography.

The method studied uses a combination of a solid-matrix dispersion partition (SMDP) followed by high-performance size-exclusion chromatography on a minicolumn (HPmSEC) of 7.8 mm I.D. for the separation of pyrethroid (PYR) residues from fatty material. The solid-matrix dispersion extraction is carried out by absorbing a fat solution onto an Extrelut-3 cartridge (filled with a macroporous diatomaceous material) and extracting the PYR residues with acetonitrile. Up to 1 g of fatty material can be extracted with 15 ml acetonitrile. The small amount (mean +/- S.D. = 12.4 +/- 5.9 mg) of fatty material which is eluted into the acetonitrile is further removed by HPmSEC. PYR pesticide residues are collected in a 2-ml fraction between 7 and 9 ml, the column being washed up to 24 ml. The two techniques used in series allow a better removal of fat, a greater input of sample and a lower consumption of solvent compared to the sole SEC on macrocolumns, and a lower limit of determination compared to the sole SEC on minicolumns. Recoveries of 9 PYR out of the 14 investigated residues from soya oil were in the range 66-83% at spiking levels ranging 0.49-2.57 mg/kg, while for 6 PYR residues tested at spiking levels in the range 0.13-0.53 mg/kg the recoveries were in the range 80-111%. Recovery of fluvalinate and permethrin could not be calculated due to interferences from soya oil, while lambda-cyhalothrin, esfenvalerate and tralomethrin gave low recovery. The final extract contains small amount (mean +/- S.D. = 2.4 +/- 0.9 mg) of lipid residue and is not completely free from interferences.

Selective clean-up applicable to aqueous acetone extracts for the determination of carbendazim and thiabendazole in fruits and vegetables by high-performance liquid chromatography with UV detection.

Fungicide residues in vegetables (benomyl, carbendazim, thiabendazole) are analyzed through a clean-up procedure that uses a portion of the aqueous acetone extract prepared for multiresidue methodology. A portion of the aqueous acetone extract (equivalent to 5 g of vegetables) is loaded onto an Extrelut-20 cartridge (the cartridge is filled with a coarse, large-pore diatomaceous material). Then, acetone is partially removed by an upward stream of nitrogen at 2l/min for 30 min. Benzimidazolic fungicides are recovered by percolating the cartridge with 100 ml of 0.1 M phosphoric acid solution, which also serves to convert benomyl to carbendazim. The percolating acid solution is drained on-line through a strong cation-exchange (SCX) solid-phase extraction cartridge with the aid of a slight vacuum. Benzimidazolic fungicides are retained on the SCX cartridge. The phosphoric acid solution is discarded together with the washings of the SCX cartridge, i.e., water followed by methanol-water (75:25), that remove unwanted coextractives. Finally, benzimidazolic fungicides are recovered by eluting the SCX cartridge with methanol-ammonium formate buffer (75:25). The final extract is then analyzed by reversed-phase HPLC with UV detection. Recoveries from crops such as apples, lettuce, strawberries and citrus fruits are generally greater than 80% and no interferences were observed. The clean-up is simple and straightforward, requires only disposable items, water solutions and a few milliliters of solvent and a minimum number of manipulations, and does not require concentration steps or electrical equipment.

Straightening: existence, uniqueness and stability.

One of the least studied universal deformations of incompressible nonlinear elasticity, namely the straightening of a sector of a circular cylinder into a rectangular block, is revisited here and, in particular, issues of existence and stability are addressed. Particular attention is paid to the system of forces required to sustain the large static deformation, including by the application of end couples. The influence of geometric parameters and constitutive models on the appearance of wrinkles on the compressed face of the block is also studied. Different numerical methods for solving the incremental stability problem are compared and it is found that the impedance matrix method, based on the resolution of a matrix Riccati differential equation, is the more precise.

Clean-up procedure for the extraction of soil samples in the determination of 2,3,7,8-tetrachlorodibenzo-p-dioxin.

This paper describes the method which was developed in relation to analytical work connected with microbial and physico-chemical degradation experiments on 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). Soil samples are best extracted with methanol plus methylene chloride. Microbial preparations are extracted with light petroleum after boiling with methanolic potassium hydroxide. The clean-up consists of a sulphuric acid treatment and chromatography on a multilayer column (Celite + H2SO4/silica gel) followed by alumina column chromatography. The clean-up procedure proved to be suitable for soil samples and microbial preparations even when large quantities of organic matter (hydrocarbons, oils, surfactants) were present.

Single-step multi-cartridge clean-up for organophosphate pesticide residue determination in vegetable oil extracts by gas chromatography.

A multi-cartridge system has been developed which, in a single step, performs the extraction and clean-up of organophosphate (OP) pesticide residues from oils and fatty extracts. A solution in hexane containing up to 1.8 g of lipidic material is loaded on to an Extrelut-3 column to which a silica-gel cartridge and a C18 silica cartridge have been connected in series. The OP pesticide residues are eluted with 15 ml of acetonitrile. Carry-over of fatty material is in the range 2-5 mg per 1.8 g of different oils, which makes the final solution amenable to capillary gas chromatography. Recoveries of 23 OP pesticides were in the range 82-111%. The whole procedure takes ca. 20 min and compares favourably with current procedures.

Screening for coumatetralyl in soft drinks by solid-matrix extraction and high-performance liquid chromatography with diode-array detection.

A method was developed for the rapid determination coumatetralyl in cola- and orange-type soft drinks, which includes extraction using solid-matrix column, clean-up by silica cartridge chromatography and reversed-phase high-performance liquid chromatography with diode-array detection. The recovery of coumatetralyl from 50 ml of soft drinks was better than 80% at spiking levels down to 50 micrograms/kg (ppb).

Application of solid-phase partition cartridges in the determination of fungicide residues in vegetable samples.

Disposable, ready-to-use cartridges filled with a macroporous diatomaceous material are used to extract in a single step fungicide residues with dichloromethane from aqueous acetone extracts of vegetables. This procedure takes the place of some functions (such as separating funnel partition, drying over anhydrous sodium sulphate and clean-up) usually performed by separate steps in classical schemes. Fourteen fungicides (dichloran, vinclozolin, chlorthalonil, triadimefon, dichlofluanide, procymidone, hexaconazole, captan, folpet, ditalimfos, iprodione, captafol, pyrazophos and fenarimol) were determined using the described procedure with recoveries between 83 and 107% at spiking levels ranging for the different compounds from 0.04 to 0.40 mg/kg. Crops subjected to the described procedure included lettuce, strawberry, apple, yellow pepper and peach, and gave extracts containing a mass of co-extractives between 5 and 30 mg. Compared with classical schemes, the described procedure is simple, less labour intensive, allows parallel handling of several extracts and does not require preparation and maintenance of equipment. Troublesome emulsions such as those frequently observed in separating funnel partitioning do not occur.