Multi-frequency shear modulus measurements discriminate tumorous from healthy tissues.

As far as their mechanical properties are concerned, cancerous lesions can be confused with healthy surrounding tissues in elastography protocols if only the magnitude of moduli is considered. We show that the frequency dependence of the tissue's mechanical properties allows for discriminating the tumor from other tissues, obtaining a good contrast even when healthy and tumor tissues have shear moduli of comparable magnitude. We measured the shear modulus G*(ω) of xenograft subcutaneous tumors developed in mice using breast human cancer cells, compared with that of fat, skin and muscle harvested from the same mice. As the absolute shear modulus |G*(ω)| of tumors increases by 42% (from 5.2 to 7.4 kPa) between 0.25 and 63 Hz, it varies over the same frequency range by 77% (from 0.53 to 0.94 kPa) for the fat, by 103% (from 3.4 to 6.9 kPa) for the skin and by 120% (from 4.4 to 9.7 kPa) for the muscle. These measurements fit well to the fractional model G*(ω)=K(iω)n, yielding a coefficient K and a power-law exponent n for each sample. Tumor, skin and muscle have comparable K parameter values, that of fat being significantly lower; the p-values given by a Mann-Whitney test are above 0.14 when comparing tumor, skin and muscle between themselves, but below 0.001 when comparing fat with tumor, skin or muscle. With regards the n parameter, tumor and fat are comparable, with p-values above 0.43, whereas tumor differs from both skin and muscle, with p-values below 0.001. Tumor tissues thus significantly differs from fat, skin and muscle on account of either the K or the n parameter, i.e. of either the magnitude or the frequency-dependence of the shear modulus.

New regime in the mechanical behavior of skin: strain-softening occurring before strain-hardening.

We report linear and non-linear shear tests on rat skin, evidencing a strain-softening regime, from 1% to 50% strain, followed by a strong strain-hardening regime, leading to a 'deck chair-shaped' stress-strain curve. The strain-softening regime was never reported as such in the literature, possibly mistaken for the linear regime in experiments starting above 1% deformation. The time-dependent response is akin to that of a gel, with a power-law frequency-dependent dynamic shear modulus ranging from ~5.6kPa to ~10kPa between 0.1Hz and 10Hz. We present an analytical non-linear viscoelastic model that accounts for both time-dependent and strain-dependent features of the skin. This eight-parameter model extends the one we proposed for parenchymatous organs by including strain-softening.

Shear mechanical properties of the porcine pancreas: experiment and analytical modelling.

We provide the first account of the shear mechanical properties of porcine pancreas using a rheometer both in linear oscillatory tests and in constant strain-rate tests reaching the non-linear sub-failure regime. Our results show that pancreas has a low and weakly frequency-dependent dynamic modulus and experiences a noticeable strain-hardening beyond 20% strain. In both linear and non-linear regime, the viscoelastic behaviour of porcine pancreas follows a four-parameter bi-power model that has been validated on kidney, liver and spleen. Among the four solid organs of the abdomen, pancreas proves to be the most compliant and the most viscous one.

On the efficiency of attachment methods of biological soft tissues in shear experiments.

Sandpaper and glue are commonly used to prevent slip of the sample in rheometric measurements of soft biological tissues. We show in this paper that the best attachment method is to glue the sample to the plates of the test device. Whereas no significant difference was observed at small strain, sandpaper proved to be less efficient than glue in preventing slip at large strain, leading to a significant underestimation of the tissue stiffness.

Shear mechanical properties of the spleen: experiment and analytical modelling.

This paper aims at providing the first shear mechanical properties of spleen tissue. Rheometric tests on porcine splenic tissues were performed in the linear and nonlinear regime, revealing a weak frequency dependence of the dynamic moduli in linear regime and a distinct strain-hardening effect in nonlinear regime. These behaviours are typical of soft tissues such as kidney and liver, with however a less pronounced strain-hardening for the spleen. An analytical model based on power laws is then proposed to describe the general shear viscoelastic behaviour of the spleen.

Dehydration effect on the mechanical behaviour of biological soft tissues: observations on kidney tissues.

This paper deals with the effects of dehydration on the mechanical properties of biological soft tissues and with the validity of methods used in previous works such as a coat of petroleum jelly or silicon oil to minimise the drying of the tissue during mechanical testing. We find that the samples get stiffer as they dry but that this phenomenon is wholly reversible upon re-hydrating the samples. A bath of saline solution is the best hydration method but a coat of low-viscosity silicon oil around the free edge of the sample also proves to be a good anti-drying method. However, using petroleum jelly to prevent tissue dehydration should be banned because the jelly largely contributes to the measured mechanical moduli.

A strain-hardening bi-power law for the nonlinear behaviour of biological soft tissues.

Biological soft tissues exhibit a strongly nonlinear viscoelastic behaviour. Among parenchymous tissues, kidney and liver remain less studied than brain, and a first goal of this study is to report additional material properties of kidney and liver tissues in oscillatory shear and constant shear rate tests. Results show that the liver tissue is more compliant but more strain hardening than kidney. A wealth of multi-parameter mathematical models has been proposed for describing the mechanical behaviour of soft tissues. A second purpose of this work is to develop a new constitutive law capable of predicting our experimental data in the both linear and nonlinear viscoelastic regime with as few parameters as possible. We propose a nonlinear strain-hardening fractional derivative model in which six parameters allow fitting the viscoelastic behaviour of kidney and liver tissues for strains ranging from 0.01 to 1 and strain rates from 0.0151 s(-1) to 0.7s(-1).

High-frequency microrheology of wormlike micelles.

We have measured the frequency-dependent shear modulus of entangled solutions of wormlike micelles by high-frequency microrheology and have compared the results with those from macrorheology experiments done on the same samples. Using optical microrheology based on laser interferometry we have measured loss and storage moduli over six decades in frequency up to about 100 kHz. We present data over a decade in concentration in the entangled regime and find good agreement between micro- and macrorheology, thus validating recently developed microrheology techniques. By collapsing data for different concentrations, we furthermore determine both the concentration scaling of the plateau modulus and a power-law exponent of the complex shear modulus at high frequencies.

Shear linear behavior of brain tissue over a large frequency range.

The literature review about the shear linear properties of brain tissue reveals both a large discrepancy in the existing data and a crucial lack of information at high frequencies associated with traffic road and non-penetrating ballistic impacts. The purpose of this study is to clarify and to complement the linear material characterisation of brain tissue. New data at small strains and high frequencies were obtained from oscillatory experiments. The tests were performed on thin porcine white matter samples (corona radiata) using an original custom-designed oscillatory shear testing device. At 37 degrees C, the results showed that the mean storage modulus (G') and the mean loss modulus (G'') increased with the frequency (0.1 to 6310 Hz) from 2.1+/-0.9 kPa to 16.8+/-2.0 kPa and from 0.4+/-0.2 kPa to 18.7+/-2.3 kPa respectively. The reliability of these new dynamic data was checked over a partially common frequency range by conducting similar experiments using a standard rheometer (Bohlin C-VOR 150). Data were also compared in the time field. From these experiments, the relaxation modulus (G(t)) was found to decrease from 24.4+/-2.1 kPa to 1.0+/-0.3 kPa between 10(-5) s and 270 s.