Barbara Gambin

Relationship between existence of energy minimizers of incompressible and nearly incompressible magnetostrictive materials

Models of incompressible and slightly compressible magnetostrictive materials are introduced. They are given by the free energy functionals which depend on magnetization and elastic deformation as well as on their gradients. We demonstrate the existence of minimum of an energy functional for a slightly compressible material. We also prove a theorem on convergence of a sequence of minimizers of less and less compressible material energy functionals to a minimizer of energy of incompressible material. Besides the existence of solution of the incompressible magnetostrictive problem is obtained.

Stochastic modelling of the eukaryotic heat shock response

The heat shock response (HSR) is a highly evolutionarily conserved defence mechanism allowing the cell to promptly react to elevated temperature conditions and other forms of stress. It has been subject to intense research for at least two main reasons. First, it is considered a promising candidate for deciphering the engineering principles underlying regulatory networks. Second, heat shock proteins (main actors of the HSR) play crucial role in many fundamental cellular processes. Therefore, profound understanding of the heat shock response would have far-reaching ramifications for the cell biology. Recently, a new deterministic model of the eukaryotic heat shock response has been proposed in the literature. It is very attractive since it consists of only the minimum number of components required by any functional regulatory network, while yet being capable of biological validation. However, it admits small molecule populations of some of the considered metabolites. In this paper a stochastic model corresponding to the deterministic one is constructed and the outcomes of these two models are confronted. The aim with this comparison is to show that, in the case of the heat shock response, the approximation of a discrete system with a continuous model is a reasonable approach. This is not always the truth, especially when the numbers of molecules of the considered species are small. By making the effort of performing and analysing 1000 stochastic simulations, we investigate the range of behaviour the stochastic model is likely to exhibit. We demonstrate that the obtained results agree well with the dynamics displayed by the continuous model, which strengthens the trust in the deterministic description. A proof of the existence and uniqueness of the stationary distribution of the Markov chain underlying the stochastic model is given. Moreover, the obtained view of the stochastic dynamics and the performed comparison to the outcome of the continuous formulation provide more insight into the dynamics of the heat shock response mechanism.

Determining temperature distribution in tissue in the focal plane of the high (>100 W/cm(2)) intensity focused ultrasound beam using phase shift of ultrasound echoes.

In therapeutic applications of High Intensity Focused Ultrasound (HIFU) the guidance of the HIFU beam and especially its focal plane is of crucial importance. This guidance is needed to appropriately target the focal plane and hence the whole focal volume inside the tumor tissue prior to thermo-ablative treatment and beginning of tissue necrosis. This is currently done using Magnetic Resonance Imaging that is relatively expensive. In this study an ultrasound method, which calculates the variations of speed of sound in the locally heated tissue volume by analyzing the phase shifts of echo-signals received by an ultrasound scanner from this very volume is presented. To improve spatial resolution of B-mode imaging and minimize the uncertainty of temperature estimation the acoustic signals were transmitted and received by 8 MHz linear phased array employing Synthetic Transmit Aperture (STA) technique. Initially, the validity of the algorithm developed was verified experimentally in a tissue-mimicking phantom heated from 20.6 to 48.6 °C. Subsequently, the method was tested using a pork loin sample heated locally by a 2 MHz pulsed HIFU beam with focal intensity ISATA of 129 W/cm(2). The temperature calibration of 2D maps of changes in the sound velocity induced by heating was performed by comparison of the algorithm-determined changes in the sound velocity with the temperatures measured by thermocouples located in the heated tissue volume. The method developed enabled ultrasound temperature imaging of the heated tissue volume from the very inception of heating with the contrast-to-noise ratio of 3.5-12 dB in the temperature range 21-56 °C. Concurrently performed, conventional B-mode imaging revealed CNR close to zero dB until the temperature reached 50 °C causing necrosis. The data presented suggest that the proposed method could offer an alternative to MRI-guided temperature imaging for prediction of the location and extent of the thermal lesion prior to applying the final HIFU treatment.

Differentiation of normal tissue and tissue lesions using statistical properties of backscattered ultrasound in breast

The aim of the study was finding the relationship between BIRADS classification combined with envelope K and Nakagami statistics of the echoes backscattered in the breast tissue in vivo and the histological data. 107 breast lesions were examined. Both, the RF echo-signal and B-mode images from the lesions and surrounding tissue were recorded. The analysis method was based on the combining data from BIRADS classifications and both distributions parameters. 107 breasts lesions - 32 malignant and 75 benign - were examined. When only BIRADS classification was used all malignant lesions were diagnosed correctly, however 34 benign lesions were sent for the biopsy unnecessarily. For K distribution the sensitivity and specificity were 78.13%, and 86.67% while for Nakagami statistics the sensitivity and specificity were 62.50% and 93.33%, respectively. Combined K and BIRADS resulted in sensitivity of 96.67% and specificity 60%. Combined BIRADS (3/4a cut-off) plus Nakagami statistics showed 100% of sensitivity with specificity equal 57.33%, decreasing the number of lesions which were biopsied from 34 to 28.

20-MHz Ultrasound for Measurements of Flow-Mediated Dilation and Shear Rate in the Radial Artery

A high-frequency scanning system consisting of a 20-MHz linear array transducer combined with a 20-MHz pulsed Doppler probe was introduced to evaluate the degree of radial artery flow-mediated dilation (FMD [%]) in two groups of patients after 5 min of controlled forearm ischemia followed by reactive hyperemia. In group I, comprising 27 healthy volunteers, FMD (mean ± standard deviation) was 15.26 ± 4.90% (95% confidence interval [CI]: 13.32%-17.20%); in group II, comprising 17 patients with chronic coronary artery disease, FMD was significantly less at 4.53 ± 4.11% (95% CI: 2.42%-6.64%). Specifically, the ratio FMD/SR (mean ± standard deviation), was equal to 5.36 × 10-4 ± 4.64 × 10-4 (95% CI: 3.54 × 10-4 to 7.18 × 10-4) in group I and 1.38 × 10-4 ± 0.89 × 10-4 (95% CI: 0.70 × 10-4 to 2.06 × 10-4) in group II. Statistically significant differences between the two groups were confirmed by a Wilcoxon-Mann-Whitney test for both FMD and FMD/SR (p <0.01). Areas under receiver operating characteristic curves for FMD and FMD/SR were greater than 0.9. The results confirm the usefulness of the proposed measurements of radial artery FMD and SR in differentiation of normal patients from those with chronic coronary artery disease.