Institute of Fundamental Technological Research

A high-frequency scanning system consisting of a 20-MHz linear array transducer combined with a 20-MHz pulsed Dopplerprobe was introduced to evaluate the degree of radial artery flow-mediated dilation (FMD [%]) in two groups of patients after5 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),wasequalto5.36×10−4±4.64×10−4 (95%CI:3.54×10−4 to7.18×10−4)ingroupIand1.38×10−4±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. (E-mail: anowicki@ippt.gov.pl) © 2018 World Federation for Ultrasound in Medicine & Biology. All rights reserved.

Flow-mediated vasodilation, Radial artery, Shear rate, Reactive hyperemia, Endothelium, Pulsed doppler, Ultrasonography

Equations of nonlinear acoustic wave motion in a non-classical lossy medium are used to derive generalised formulas describing the phenomena of reflection and transmission. Integral, non-local operators that are caused by the nonlinear effects in wave propagation and occur in reflection and transmission formulas are given in a form in which classical linear reflection and transmission coefficients are explicitly separated. Numerical calculations are performed for a simplified, one-dimensional wave travelling in a lossless medium. These simplifications reveal the pure effect of the impact of nonlinearities on the reflection and transmission phenomena. We consider adjacent media with different properties to illustrate various aspects of the problem. In particular, even if two media have the same linear impedance and the same material modules of the third order, we observe an explicit effect of the nonlinearity on the reflection phenomenon. The theoretical predictions are confirmed qualitatively by numerical calculations based on the finite difference time domain method.

Non-linear sound wave, Non-linear reflection, Non-classical absorption, Soft tissues

Temperature monitoring is essential for various medical treatments. In this work, we investigate the impact of temperature on backscattered ultrasound echo statistics during a high intensity focused ultrasound treatment. A tissue mimicking phantom was heated with a spherical ultrasonic transducer up to 56 _C in order to imitate tissue necrosis. During the heating, an imaging scanner was used to acquire backscattered echoes from the heated region. These data was then modeled with the homodyned K distribution. We found that the best temperature indicator can be obtained by combining two parameters of the model, namely the backscattered echo mean intensity and the effective number of scatterers per resolution cell. Next, ultrasonic thermometer was designed and used to create a map of the temperature induced within the tissue phantom during the treatment

Temperature monitoring, homodyned K distribution, focused ultrasound

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/cm2. 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.

Ultrasonic temperature imaging, HIFU, Echo phase shift, Velocity image contrast

Texture of ultrasound images contain information about the properties of examined tissues. The analysis of statistical properties of backscattered ultrasonic echoes has been recently successfully applied to differentiate healthy breast tissue from the benign and malignant lesions. We propose a novel procedure of tissue characterization based on acquiring backscattered echoes from the heated breast. We have proved that the temperature increase inside the breast modifies the intensity, spectrum of the backscattered signals and the probability density function of envelope samples. We discuss the differences in probability density functions in two types of tissue regions, e.g. cysts and the surrounding glandular tissue regions. Independently, Pennes bioheat equation in heterogeneous breast tissue was used to describe the heating process. We applied the finite element method to solve this equation. Results have been compared with the ultrasonic predictions of the temperature distribution. The results confirm the possibility of distinguishing the differences in thermal and acoustical properties of breast cyst and surrounding glandular tissues.

medical ultrasound, temperature changes in vivo, breast tissue, ultrasonic temperature measurement

Polyvinyl-alcohol cryogel is commonly used for soft tissue phantom manufacture. The gel formation from an aqueous solution of polyvinyl-alcohol takes place during the freezing and thawing cycle. The aim of this work was to assess the degree of gel solidification, hence the material stiffness, by means of quantitative ultrasound. We manufactured three phantoms which differed in the number of freezing/thawing cycles. First, tissue phantoms were examined with an elastography technique. Next, we measured the speed of sound and the attenuation coefficient. What is more, the inter structure variations in phantoms were assessed with the Nakagami imaging which quantifies the scattering properties of the backscattered ultrasound echo. Obtained results confirmed the connection between the number of freezing/thawing cycles and the solidification process. We defined the boundary layer as a region which has a different structure than the sample interior. Next, for each phantom this layer was extracted based on a Nakagami parameter map. We calculated that the thickness of the boundary layer was lower in samples which were subjected to a larger number of freezing/thawing cycles.

soft tissue phantoms, elastography, ultrasound attenuation, speed of sound, Nakagami maps, stiffness

Therapeutic and surgical applications of High Intensity Focused Ultrasound (HIFU) require monitoring of local temperature rises induced inside tissues. It is needed to appropriately target the focal plane, and hence the whole focal volume inside the tumor tissue, prior to thermo-ablative treatment, and the beginning of tissue necrosis. In this study we present an ultrasound method, which calculates the variations of the speed of sound in the locally heated tissue. Changes in velocity correspond to temperature change. The method calculates a 2D distribution of changes in the sound velocity, by estimation of the local phase shifts of RF echo-signals backscattered from the heated tissue volume (the focal volume of the HIFU beam), and received by an ultrasound scanner (23). The technique enabled temperature imaging of the heated tissue volume from the very inception of heating. The results indicated that the contrast sensitivity for imaging of relative changes in the sound speed was on the order of 0.06%; corresponding to an increase in the tissue temperature by about 2 °C.

HIFU, echo phase shift, parametric imaging, velocity/brightness CNR

The aim of this work was to find the differences between random media by analyzing the properties of the ultrasound signals backscattered from the inhomogeneities. A numerical model is used to generate two types of random media. The first has the randomness in scatterers’ positions and the second has the randomness in the size and acoustical properties of scatterers. The numerical model of wave scattering has been used to simulate the RF (radio frequency) signals caused by the incident pulse traveling as a plane wave. The markers of randomness type differences between the scattering media were obtained with the help of the spectral and wavelet analysis. The effect of differences in randomness type is more spectacular when the wavelet analysis is performed.

spectrogram, scalogram, wavelets, random scattering structure

The paper deals with the elastic and cohesive interface behavior of pre-cracked bi-material ceramic-metal structures under dynamic time harmonic load. The shear lag model as well as the Fourier method is applied to find the dynamic response of the considered bi-material structure, assuming the cohesive interface behaviour, accompanied before of the elastic-brittle one. In both cases, the growth of debond length is not considered, e.g. at a given loading condition the only corresponding debond length is found. The inertia forces of the already elastic debond parts of the bi-material structure are neglected. Appropriate contact conditions are proposed in order to fit together both elastic and cohesive solutions. The numerical predictions for the cohesive debond length of the bi-material structures is calculated by the aid of the corresponding value of the elastic debond length at the same loading condition. The influence of loading characteristics i.e. frequencies and amplitude fluctuations on the debond length and the interface shear stress distribution is discussed. The parametric analysis of the results obtained is illustrated by examples of the modern ceramic-metal composites on metal substrates and is depicted in figures.

Dynamic behaviour of bi-material structure, cracked plate, shear lag model, elastic-brittle and cohesive interface delamination, debond length

A novel estimation of temperature changes inside soft tissues has been proposed in sub-ablation range, i.e. 20°C-48°C. This estimation has been obtained by studying statistical properties of backscattered ultrasonic signals. Two different procedures of heating/cooling have been performed in which the RF echoes have been registered from soft tissue phantom in the first procedure, and from soft tissue in vitro in the second one. Calculated envelopes of signals registered in time points during heating/cooling experiments have been treated as a statistical sample drawn from a random variable with three different distributions, namely the Rayleigh distribution, the Nakagami distribution, and the K-distribution. The histograms obtained in subsequent time moments have been fitted to the three distributions. Dependencies of their shape and scale parameters on temperature have been calculated. It is concluded that the shape parameter of the K-distribution can be chosen as the best marker of temperature changes in both experiments. The choice of the marker has been made by analysis of temperature dependencies of all calculated parameters and by comparing the quality of fitting all histograms to the considered distributions. Besides, the chosen marker as a function of temperature exhibits the closest shape to temperature/time function experimentally measured.

therapeutic applications, ultrasonics, medical imaging

There are two main topics of this research: (i) one topic considers overall properties of a nonlinear cellular composite, treated as a model of the liver tissue, and (ii) the other topic concerns the propagation of heat in the nonlinear medium described by the homogenised coefficient of thermal conductivity.

For (i) we give a method and find the effective thermal conductivity for the model of the liver tissue, and for the point (ii) we present numerical and analytical treatment of the problem, and indicate the principal difference of heat propagation in linear and nonlinear media. In linear media, as it is well known, the range of the heat field is infinite for all times t > 0, and in nonlinear media it is finite.

Pennes’ equation, which should characterize the heat propagation in the living tissue, is in general a quasi-nonlinear partial differential equation, and consists of three terms, one of which describes Fourier’s heat diffusion with conductivity being a function of temperature T . This term is just a point of our analysis.

We show that a nonlinear character of the medium (heat conductivity dependent on the temperature) changes in qualitative manner the nature of heat transfer. It is proved that for the heat source concentrated initially (t = 0) at the space point, the range of heated region (for t > 0) is finite. The proof is analytical, and illustrated by a numerical experiment.

heat transport, asymptotic homogenisation, effective heat conductivity

Different ultrasound echoes properties have been used for the noninvasive temperature monitoring. Temperature variations that occur during heating/cooling process induce changes in a random process of ultrasound backscattering. It was already proved that the probability distribution of the backscattered RF (radio frequency) signals is sensitive to the temperature variations. Contrary to previously used methods which explored models of scattering and involved techniques of fitting histograms to a special probability distribution two more direct measures of changes in statistics are proposed in this paper as temperature markers. They measure the ”distance” between the probability distributions. The markers are the Kolmogorov Smirnov distance and Kulback-Leiber divergence. The feasibility of using such nonparametric statistics for noninvasive ultrasound temperature estimation is demonstrated on the ultrasounds data collected during series of heating experiments in which the temperature was independently registered by the classical thermometer or thermocouples.

ultrasoud echoes, non-invasive temperaturę monitoring, Kolmogorov Smirnov distance, Kulback-Leiber divergence

The study shows the direct relationship between the temperature field and the parallel changes that are taking place in backscattered ultrasonic signals from the breast tissue in vivo when heated to the temperature of approximately 42 o C. The non-uniform temperature field inside the heating tissue was determined by the numerical model using FEM. It is shown that the spatial distribution of intensities of the backscattered signals coincides with the temperature distribution field predicted by the numerical model in some areas. The result indicates the possibility of the indirect measurement of the temperature rise in the breast tissue in vivo by measuring the intensity variations of the ultrasound echo.

temperature field, backscattered ultrasonic signals, breast tissue in vivo, FEM model

The comparison between theoretical and numerical solutions of the reflection/transmission problem for the acoustic plane wave normally incident on the discontinuity surface between two nonlinear lossy media was presented. Numerical calculations made under the assumption that the two media have the same impedance, allow to single out the effect of nonlinearities in the description of the reflection and transmission phenomena, so they agreed with theoretical predictions. It was shown that theoretically obtained and numerically calculated results mutually confirmed themselves

Nonliear reflection, transmission, Riccati equation

In the paper the concept of synthetic aperture used for high resolution/high frame rate ultrasonic imaging is reviewed. The synthetic aperture technique allows building extended “virtual” apertures, synthesized from smaller real aperture resulting in improved lateral resolution along full penetration depth without sacrificing the frame rate.

Especially, four methods, synthetic aperture focusing (SAF), multi-element synthetic aperture focusing (M-SAF), synthetic receive aperture (SRA) and synthetic transmit aperture (STA) are addressed. The effective aperture function, describing two-way, far field radiation is a useful tool in beam pattern analysis. Some basic notations, which are used to calculate the effective aperture are introduced in Appendix.

synthetic aperture, effective aperture, ultrasonography

The aim of the paper is to find links between the dynamics of changes of statistical parameters and changes in spectral properties of the signal envelope of backscattered RF signals during the thermal process. We have shown previously that by using wavelet approximations these tendencies are better recognized in the case of the heating of a phantom sample than in the parallel analysis performed for a full signal envelope. Here we are currently expanding this statement to the case of heating a soft tissue sample in vitro. The shape parameter of the K- distributed random variable is considered as a statistical marker of temperature level changes. Additionally, the spectral properties of different levels of wavelet approximations are calculated and their sensitivity to temperature increase and decrease is demonstrated. Both approaches registering changes in temperature, are used in the case of the pork loin tissue sample in vitro, heated by an ultrasound beam with a different power.

ultrasound echoes, soft tissue sample in vitro, statistical marker of temperaturę rise

Two heating protocols for soft tissue phantoms have been performed. An Agar-Gel-Oil (AGO) mixture has been heated locally by applying ultrasonic beams and a Poly Vinyl Alcohol-cryogel (PVA-c) has been heated “globally” by a water bath with a controlled temperature rise. The RF signals were collected during heating by an ultrasound transducer to ensure no interference from waves from the heating transducer. Independently, the thermocouples' measurement has been used to obtain temperature as a function of time in the AGO case. At first, a compensation of attenuation was performed and normalized envelopes of signals were used as data for statistical analysis. It is shown that random the values of the backscattered amplitude are close to Rayleigh and K-distributed random variables for AGO and PVA-c, respectively. Temperature is linked to the scale parameter of Rayleigh distribution for the AGO, and the shape parameter of K-distribution for PVA-c were calculated and discussed in the context of their suitability for the acoustic measurement of temperature.

Agar-Gel_Oil soft tissue phantom, K-distribution shape parameter, temperaturę measurements

The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ -convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.

gamma-convergence, incompressibility, magnetostrictive material, second gradient of deformation, existence of minimizers

For the study of the temperature increase in the soft tissues irradiated by a low-power ultrasound [1], soft tissue-mimicking materials can be used. The phantoms have been produced based on an aqueous solution of agar, oil, and glass beads microparticles. The RF signals collected in the experiments enabled evaluation of the acoustic properties of phantoms with different number of strong scatterers (concentration varied from 0 to 30 pcs/mm3). Speed of sound (SOS) determined for the phantoms was similar to the value typical of soft tissue (about 1540 m/s). To determine attenuation coefficient the semi-transmission method has been used. Attenuation coefficient value varied from 0.5 to 1.1 dB/(MHz cm), depending on the number of scatterers. It was shown that the phantoms stored for 6 months preserved their acoustical properties and were usable for further experiments. It was found that within the total attenuation, the part corresponding to scattering can be distinguished.

acoustical characteristics, soft tissue mimicking material, scatterers number

The paper contains the wavelet approach to registered backscattered RF signals from two different cases. First, the wavelet analysis has been performed for RF signals registered from soft tissue phantoms .The second case is the wavelet analyses of RF scattered signals from regions of healthy and BCC changed human skin. The three phantoms made from tissuemimicking material with different structures have been measured. We claim that there are visible differences in the statistical parameters of wavelets coefficients of signals between healthy and BCC changed skin regions as well as between phantoms without scatterers and with different number of strong small scatterers.

backscattered RF signals , skin cancer differentiation, scatterers numer, wavelet approximations

The interface cohesive behaviour and interface delamination in a bi-material structure consisting of two plates and material interface with zero thickness under time harmonic load is studied. Previously, the authors studied the elasto-brittle interface behaviour, from both sides of a crack, initially normal to the interface, when the elastic-brittle interface debonding appeared. Now, it is again assumed that the restriction for the ratio of energy release rates of the second plate and interface allowing the occurrence of an interface cohesive delamination before the initiation of the normal crack in the second plate is satisfied. The shear lag model is adopted and applied to find the dynamic response of the considered structure, assuming the cohesive interface behaviour, accompanied before of the elastic-brittle one. In both cases, the growth of debond length is not considered e.g. at a given loading condition the corresponding single debond length is found. The inertia forces of the already debonded interface elasto-brittle cracks (mode II) are neglected. The appropriate contact conditions are proposed in order to fit together both elastic and cohesive solutions. The Laplace inverse transform is applied to obtain the original of cohesive debond length by the aid of the already obtained elastic value of debond length at the same loading condition. Parametric analysis of the results obtained is illustrated by examples of the modern ceramic-metal composite on metal substrate. The influence of frequencies and amplitude fluctuations on the cohesive debond length and the interface shear stress distribution are discussed.

dynamic behaviour of bi-material structure, cracked plate, shear lag model, Laplace transform, cohesive interface delamination, cohesive debond length

In this presentation we consider hyperthermia, a procedure of raising the temperature above 43 C, as a treatment modality. To this purpose, a numerical model of in vivo soft tissue ultrasound heating is proposed by extending a previously presented in vitro model. Based on the numerical simulations, a heating scheme satisfying some constraints related to potential clinical applications is established, and the resulting temperature time-course profile is composed with the temperature-dependent protein denaturation formula of a recently published mathematical model for the eukaryotic heat shock response. The obtained simulation results of the combined models are discussed in view of potential application of ultrasound soft tissue heating in clinical treatment.

Hyperthermia, Heat Shock Response dynamics, Ultrasound therapeutic treatment, mathematical modelling

The behavior of a precracked bi-material structure interface under given static and dynamic axial loading is an interest object in the present paper. Firstly, it is shown that the shear-lag model is a proper tool to analyze a delamination process in a precracked bi-material structure undergoing static loading. Secondly, the “shear-lag model” is applied to the structure under dynamic loading. To solve the problem for an interface delamination of the structure and to determine the debond length along the interface, our own 2D boundary element method (BEM) code is proposed in the case of static loading, and the shear-lag model together with the Laplace transforms and half-analytical calculations are used in the case of dynamic loading. The interface layer is assumed as a very thin plate compared with the other two. The parametric (geometric and elastic) analysis of the debond length and interface shear stress is done. The results from the 2D BEM code proved the validity of analytical solutions to the shear-lag model. In the dynamic case, the influence of loading characteristics, i.e., frequencies and amplitude fluctuations on the shear stress and the value of debond length for an interval of time, is discussed. The analysis of the obtained results is illustrated by an example of the modern ceramic-metal composite, namely cermet, and depicted in figures.

Debond length, Precracked bi-material structure, Shear-lag model, Delamination, BEM

The interface behaviour between two layers of 2D elastic structure under dynamic time-harmonic load is studied. The “shear lag model” is adopted and applied to the dynamic response of bi-material structure, assuming the elastic-brittle behaviour of the interface. The Laplace transforms together with half-analytical calculations are used to obtain the shear stress and elastic debond lengths along the interface at sinusoidal load. Parametric analysis of the obtained results is illustrated by an example of the modern ceramic-metal composite, so called cermet, and depicted in figures. The influence of loading characteristics, i.e. frequencies and amplitude fluctuations on the shear stress and the value of debond length for a small interval of time, is discussed.

Dynamic behaviour of bi-material structure, cracked plate, shear lag model, elastic-brittle interface delamination, debond length

The aim of this work is mathematical modeling and numerical calculation in space and time of temperature fields induced by low power focused ultrasound beams in soft tissue in vivo after few minutes exposure time. These numerical predictions are indispensable for planning of various ultrasound therapeutic applications. Both, the acoustic pressure distribution and power density of heat sources induced in tissue, were calculated using the numerical solution to the second order nonlinear differential wave equation describing propagation of the high intensity acoustic wave in three-layer structure of nonlinear attenuating media. The problem of the heat transfer in living tissues is modelled by the Pennes equation, which accounts for the effects of heat diffusion, blood perfusion losses and metabolism rate. Boundary conditions and geometry are chosen according to the anatomical dimensions of a rat liver. The obtained results are compared with those calculated previously and verified experimentally for temperature elevations induced by ultrasound in liver samples in vitro. The analysis of the results emphasizes the value of the blood perfusion and the values of heat conductivity on the temperature growth rate. The numerical calculations of temperature fields were performed using the ABAQUS FEM software package. The thermal and acoustic properties of the liver and water being the input parameters to the numerical model were taken from the published data in cited references. The range of thermal conductivity coefficient of living tissue is obtained from the model of two-phase composite medium with given microstructure. The first component is a “solid” tissue and the second one corresponds to blood vessels area. The circular focused ultrasonic transducer with a diameter of 15 mm, focal length of 25 mm and resonance frequency of 2 MHz has been used to generate the pulsed ultrasonic beam in a very introductory experiment in vivo, which has been performed. Numerical prediction confirms qualitatively its results.

focused ultrasound, soft tissues, local thermal fields, numerical modelling

The behaviour of the interface of a pre-cracked bi-material ceramic-metal structure under static axial loading is an object of interest in the present paper. To solve the problem for interface delamination of the structure and to determine the debond length along the interface, a 2D BEM code was created and applied. The interface plate is assumed as a very thin plate comparing with the others two. The parametric (geometric and elastic) analysis of the debond length and interface shear stress is done. First, the obtained numerical results are compared with analytical ones from 1D. Shear lag analysis of the considered structure. The respective comparison is illustrated in figures and shows a good agreement. The comparison between the calculated using 2D BEM code elastic-brittle debond lengths with Song's experimental data for the bi-material structure Zinc/Steel as well as with respective results from FEM simulation shows good coincidence.

BEM, Shear lag analysis, bi-material structure, debond length

Some aspects of FEM modeling of hyperthermia, the procedure of tissue temperature rise above 37 oC inside the living organism, as a treatment modality, are studied. Low intensity focused ultrasound (LIFU) beam has been used as a source of temperature rise in the liver tissue during performed experiments in vitro. The comparison of the FEM model of the corresponding heating process and the experimental results has been presented in [1]. In the paper, the FEM model of heating scheme of the rat liver tissue in vivo irradiated by the same ultrasound transducer is formulated. At first, the existence of blood perfusion is taken into account in the model equation. Secondly, the thermal and acoustical properties, which are the input parameters of the numerical model, are taken from the published data in literature. Here, the size and the intensity of heat sources are modeled in two ways on the basis of acoustic nonlinear equation solutions in 3 layers attenuating medium. We demonstrate how the results of FEM model in the case of in vitro and in vivo heating, depend on the assumed power density of heat sources, as well as on the size of the heated area. The results are compared and discussed. The influence of different models on temperature rise profiles are demonstrated.

Some important details of the Backscatter Effective Cross-Sections (BECS) obtained for random scattering structures (like trabecular bone) are explain by comparison with the results obtained by means of the simplified theoretical model. The simplified model was (establish) and justified on the basis of the structural analysis of the results obtained for exact model of the field scattering on complex structures. The simplified model is commonly used in description of the scattering on the regular structures like crystal. Comparison with experimental results for the trabecular bone is also presented. The results allowed to conclude that crystallographic methods could be potentially useful for extracting characteristic features of trabecular bone.

Multi scattering, Random structures

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.

Stochastic model, Computer simulations, Markov chain, Gillespie algorithm, Stationary distribution

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 minimize of energy of incompressible material. Besides the existence of solution of the incompressible magnetostrictive problem is obtained.

micromagnetics, magnetostrictive material, incompressible, nearly incompressible materials, existence problem

The aim of this work is twofold. Firstly, to verify a theoretical model which is capable of predicting temperature fields appearing in soft tissues during their ultrasound treatment. Secondly, to analyze some aspects of the dynamics of Heat Shock Response induced by the heating process in the context of therapeutic treatment. The theoretical investigations and quantitive analysis of temperature increments at any field point versus time of heating process, depending on the heat source power, spatial distribution and duration as well as on the tissue thermal properties, has been carried out by Finite Element Method (FEM). The validation of the numerical model has been performed by comparison of the calculation results with the experimental data obtained by measuring in vitro of the 3D temperature increments induced in samples of the turkey and veal liver by the circular focused transducer with the diameter of 15 mm, focal length of 25 mm and resonance frequency of 2 MHz. Various ultrasonic regimes were considered. They were controlled by adjusting ultrasound power and exposure time. The heat shock proteins (HSP) and misfolded proteins (MFP) levels during the proposed cyclic sonification are presented.

heat-responsive gene therapy, temperature field, low-power focused ultrasound, soft tissues, ultrasonic regime control, heat sources distribution, heat shock proteins

A novel high-frequency scanning system, with a 20-MHz linear array transducer combined with 20-MHz pulsed Doppler, was introduced to evaluate the degree of radial artery flow-mediated dilation (FMD) and shear rate (SR)-normalized FMD (FMD/SR) after 5 min of reactive hyperaemia. In group I, comprising 27 healthy volunteers, FMD was 15 ± 4.8%, and in group II, comprising 17 patients with coronary artery disease, FMD was significantly smaller, being equal to 4.6 ± 4%. FMD/SR was equal to 5.365 ± 4.835·10-4 in group I and 1.3 ± 0.89·10-4 in group II. Statistically significant differences between the two groups were confirmed by Wilcoxon-Mann-Whitney test for FMD and FMD/SR (p-values < 0.01). AUCs of ROC 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 subjects from those with atherosclerotic lesions.

flow mediated vasodilation, radial artery, shear rate, reactive hyporaemia, endothelium, pulsed Doppler, ultrasonography.

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.

breast cancer, quantitative ultrasound, BIRADS

The Ultrasonix SonixTouch scanner with the special RF block was used to collect Bmode images together with appropriate RF echoes from the pathological and healthy breasts regions of patients with diagnosed malignant and benign breast lesions. The RF data were processed for the statistics of the backscattered echo signals assessment (K distribution and effective density of scatterers – M and Nakagami distribution and its shape parameter m). The comparison of signals recorded from malignant and healthy tissues showed, that in 80% of examined cases the values of the statistical parameters M were higher for carcinomas tissues than for healthy tissue. Beside of that in the case of benign lesions obtained results was able to distinguish the fibroadenoma from the other with probability of 75%.

quantitative ultrasound, breast cancer, statistics

The goal of this study was to find the macroscopic characteristics of the random nature of ultrasonic backscattering signals which would be sensitive to the temperature changes. The sample made of Polyvinyl Alcohol – Cryogel (PVA-C, the pre-freezing in one cycle aqueous solution of PVA) was heated in a water bath starting from the room temperature up to the temperature below the soft tissue ablation temperature. The RF signals were collected during the heating/cooling process and the signals envelopes had been calculated. The wavelet approximation of subsequent level worked as a low-pass filter what qualitatively improved the temperature estimating. The latter was realized by observing the variations of the shape parameter of K-distribution. The trend of the shape parameter variation with temperature was calculated including the wavelet decomposition and was compared with the real temperature changes measured by the thermometer. We have found that tracking changes in echoes envelope statistics allows to distinguish between heating and cooling process, and determine the time required to reach maximum temperature.

random signals, Polyvinyl Alcohol – Cryogel, wavelet approximation, temperaturę monitoring

The work concerns in finding the ultrasonic characteristics of temperature changes within the heated region of two types of samples: phantom sample made from PVA (Polyvinyl Alcohol Cryogel) and soft tissues sample in vitro. We are looking for changes in the statistical parameters of the backscattered signals registered during two different heating procedures for the two types of samples. We are looking for statistical distributions describing the statistics of the signal envelope received during the experiments heating/cooling. Matching of the histogram to the different probability density functions of Rayleigh, Gamma, Nakagami and K-distribution was analyzed by calculating the mean square error. Besides, the dependence on temperature changes of characteristic parameters for considered distributions have been calculated. We conclude that the shape parameter of K-distribution is the best statistical marker of a temperature level in the performed experiments.

therapeutic applications, ultrasonics, medical imaging

Terapeutyczne i chirurgiczne zastosowania ogniskowych ultradźwięków wymagają monitorowania lokalnych zmian temperatury w tkance. Najkorzystniejsze z punktu widzenia użytkowego i ekonomicznego byłoby zastosowanie do tych celów technik ultradźwiękowych.
Praca przedstawia próbę zastosowania metody estymacji przemieszczenia ech do monitorowania zmian temperatury podczas ultradźwiękowego nagrzewania tkanki in vitro. Dane uzyskane drogą pomiarów ultradźwiękowych zostały przetworzone w celu wyznaczenia mapy przemieszczeń ech i odniesione do pomiarów rozkładu temperatury przeprowadzonych za pomocą termopar. Uzyskane wyniki umożliwiają ocenę pola temperatury i pozytywnie rokują połączeniu ultradźwiękowych technik nagrzewania i szacowania lokalnej temperatury tkanki.

obrazowanie temperatury, prędkość akustyczna

W pracy przedstawiono wstępne wyniki pomiaru pola temperatury wewnątrz tkanki in vitro w czasie procesu nagrzewania wiązką ultradźwiękową o słabej mocy oraz pomiaru właściwości akustycznych wzorców tkanek miękkich. Wzorce te zbudowano w celu dalszych badań nad powiązaniem wzrostu temperatury z właściwościami akustycznymi, gdyż próbki tkankowe in vitro okazały się niepowtarzalne i nietrwałe. Na wykonanych 3 wzorcach tkankowych dokonano pomiaru sygnału przejścia i wyznaczono prędkość propagacji impulsu, współczynnik tłumienia oraz zbadano statystykę rozproszenia. Przedyskutowano wpływ liczby elementów rozpraszających na te wielkości.

wzorce tkanek, sygnał ultradźwiękowy, prędkość dźwięku, tłumienie, statystyka rozproszenia

Therapeutic and surgical applications of focused ultrasound require monitoring of local temperature rises induced inside tissues. From an economic and practical point of view ultrasonic imaging techniques seem to be the best for a temperature control. In this work an attempt to apply the method of the ultrasonic echoes displacement estimation for monitoring local temperature rises in tissues during their heating by focused ultrasound is presented. The estimated temperature rise was compared with this measured by a thermocouple. The obtained results enable to evaluate the temperature fields induced in tissues by pulsed focused ultrasonic beams using non-invasive imaging ultrasound technique.

HIFU, therapeutic ultrasound, ultrasonic imaging, echo strain estimation

W pracy rozpatrzono modelowanie hipertermii, to jest procedury podwyższania temperatury powyżej 37 oC w celach terapeutycznych. Skoncentrowana wiązka ultradźwiękowa niskiej mocy była poprzednio wykorzystywana jako źródło ciepła w tkance wątroby w doświadczeniach przeprowadzanych in vitro. Do generowania impulsu wiązki ultradźwiękowej został użyty okrągły skupiający przetwornik piezoelektryczny o średnicy 15 [mm], długości ogniskowej 25 [mm] i częstotliwości rezonansowej 2 [MHz]. Eksperymentalne dane wzrostu temperatury mierzone przez termopary, zostały porównane z wynikami obliczeniowymi otrzymanymi z modelu numerycznego bazującego się na metodzie elementów skończonych. W tej pracy użyto metody elementów skończonych do obliczenia procesu nagrzewania tkanek in vivo. Po pierwsze, w modelowaniu została uwzględniona perfuzja krwi, jako ujemne źródła ciepła zależne liniowo od przyrostu temperatury. Po drugie, właściwości termiczne i akustyczne tkanki używane w modelu numerycznym zastały przyjęte z opublikowanych danych, podczas gdy rozmiar i intensywność źródeł ciepła modelowane są w zgodzie z wynikami uzyskanymi z rozwiązań nieliniowego równania propagacji fali akustycznej w trójwarstwowym ośrodku stratnym. Pokazano, że wyniki modelu numerycznego procesu nagrzewania w tkance in vivo silnie zależą od gęstości mocy cieplnej źródeł oraz od rozmiaru obszaru nagrzewania. Źródła ciepła aproksymowano numeryczne na dwa różne sposoby. Pierwszy, polegał na modelowaniu źródeł ciepła, jako jednorodnego rozkładu gęstości mocy cieplnej rozłożonej w objętości 3 cylindrów imitujących kształt wiązki akustycznej. Drugi sposób przyjmuje ciągły, niejednorodny rozkład gęstości mocy uzyskany bezpośrednio z numerycznego rozwiązania przez odpowiednio dobrane aproksymanty Padé (funkcje wymierne). Wyniki są porównywane i omówione. Pokazano wpływ różnych modeli na profile wzrostu temperatury.

Poly(vinyl alcohol) cryogel, PVA-C, is produced as a soft tissue-mimicking material, suitable for application in ultrasound imaging. A 10% by weight poly(vinyl alcohol) in water solution was used to form PVA-C, which is solidified through a freeze–thaw process. The number of freeze–thaw cycles affects the properties of the material, particularly the mechanical stiffness. The ultrasound characteristics were investigated using 3 different cylindrical samples of PVA-C produced by 1, 2 and 3 cycles of freezing-thawing process. The speed of sound was found to range from 1502 to 1522 m s−1, and the attenuation coefficients were in the range of 0.085–0.124 dB/(cm MHz). The structural eterogeneities are visualized by Nakagami maps and it is shown that the range of Nakagami parameter characterize the differences between samples. The samples are structurally different in the regions close to the surface from the internal regions. This is probably caused by the spatial heterogeneity of the solidification process. The thickness of the boundary layer is also measured from Nakagami maps and it is shown that it is also linked to the type of samples. The elastography maps (measured by the commercial quasistatic strain imaging system . . . ) are compared with Nakagami maps. The question arises, in what circumstances parametric estimation of spatial structure variations by Nakagami maps are linked to the spatial variations of local stiffness?

soft tissue phantoms, elastography, ultrasound attenuation, speed of sound, Nakagami maps, stiffness

soft tissue phantoms, backscattered ultrasonic signal, changes in the backscattered energy

The practical aim of this research is to detect the temperature by the selected properties of the backscattered ultrasound signals collected during heating/cooling of the soft tissue sample. The initial data are the raw backscattered signals, RF (radio frequency) signals, which form the two-dimensional matrix. These data are divided according to the regions of interest (ROI) analyzed piece-wise in the following way:
• absolute value of Hilbert transform in each time sample is calculated,
• the approximations with Daubeschies 6 wavelets is performed,
• Kolmogorov-Smirnov distance and Kullback-Laibler divergence between initial ROI statistics and the statistics of the ROI in succesive temperature level are used to visualization of the dynamic temperature changes on the map of the sample volume.

temperaturę detection, non-parametric statistics, backscattered ultrasound, wavelet

The scattering is the fundamental phenomena used for US imaging of specific organs. In this study the method searching for best fitted statistical distribution of the acquired echoes from the breast tissue is discussed, especially addressing the ‘‘effective’’ number of scatterers. The aim of the study was finding the relationship between the specific properties of statistics of envelope of the ultrasonic echoes backscattered in the breast tissue in vivo, and its morphological properties for normal tissue and the pathological lesions.
Methods: 72 patients with 83 suspicious breast lesions (BIRADS 3, 4, 5) were examined. The analysis method was based on the parametric imaging representing a map of local statistical properties of the scattering of ultrasound waves in normal and pathological tissues. Both, the RF echo-signal and B-mode images from the lesions and surrounding tissue were recorded. The statistics of backscattered speckle-like echoes envelopes were modelled using K and Nakagami distributions. For all lesions the set of sub-ROIs covering full lesion was chosen. The statistical analysis was done for every sub-ROI separately. The shape parameters were calculated including the compensation for TGC applied and for the attenuation.
Results: The evaluation of all 83 breasts lesions revealed 23 malignant and 60 benign lesions. Typically, both, shape parameters for malignant lesions were statistically larger than for surrounding tissue. On the other hand, the benign lesions revealed much larger variance of the parameters comparing to the surrounding and malignant tissue. The sensitivity and specificity of B-mode imaging with the cut-off points BIRADS-4a/4b were 93%, 86%. For K and Nakagami distributions obtained sensitivity and specificity were respectively 85% and 91%.
Conclusions: The quantitative measurements of the breast tissue backscattering statistical properties improve the specificity of B-mode examinations and can be helpful in the differentiation the character of the breast lesions. It was proved that the range of the shape parameters appears to be rather large and can not be interpreted without taking into account the corresponding values in the surrounding ‘‘normal’’ tissue.

breast cancer, ultrasound, RF echo-signal

Numerical analysis of the reflection/transmission problem for a non-linear acoustic wave is studied. The wave is a plane wave and it is incident normally on the plane discontinuity surface between two lossy media. Numerical calculations are proceeded with the help of self written software (in Fortran). The influence of different propagation parameters (properties of two different media) on the reflected and transmitted wave fields are discussed. Particularly, it is shown that although two media have the same impedance, the effect of the propagation nonlinearities is still existing in the reflected and transmitted fields. The performed analysis qualitatively confirmed theoretical predictions quite well.

Nonliear reflection, transmission, Riccati equation, Numerical caslculations

After discovery of strong sonar systems, it was realized that the high intensity ultrasound waves can be dangerous for biological organisms. This observation led to research in tissue heating effects. The liver tissue from mathematical point of view can be considered as a micro-periodic cellular medium, and in circumstances justified by biological reasons, the mathematical methods of homogenisation developed for micro-periodic media can be applied to determine some overall properties of the tissue. Fourier’s heat diffusion term in Pennes’ equation is the point of departure in our analysis, . The liver, the largest internal organ in the human body, is connected to two large blood vessels, the hepatic artery and the portal vein. The hepatic artery carries oxygen-rich blood from the aorta, whereas the portal vein carries blood rich in digested nutrients from the entire gastrointestinal tract and also from the spleen and pancreas. These blood vessels subdivide into small capillaries known as liver sinusoids, which then lead to a lobule. A hepatic lobule is a small division of the liver defined at the histological scale. The lobules are arranged into an hexagonal lattice.
We have evaluated the dependence of effective conductivity λeff for the composite consisting of the basic cells arranged in a two-dimensional periodic system and built of the collagen capillaries filled with the water. Analytical and numerical results are going to be verified by measurement of temperature using magnetic resonance imaging (MRI) and through measurement of backscattered ultrasound waves.

liver tissue, Pennes’ equation, heat transport, asymptotic homogenization, effective coefficients

Tissue mimicking materials for ultrasound research, phantoms, should be acousticaly similar to the tissues. Such requirements are filled by the AGO (agar-oil) phantoms. Here, they have been used in experiment of heating internal region of samples by the high intensity ultrasound (HIFU) transducer. During heating the RF (radio frequency) ultrasound signals have been collected. It is demonstrated that the temperature changes in AGO phantoms can be described by the special properties of the backscattered RF signals, namely the shape parameter of the Nakagami distribution and SNR (signal to noise ratio) of signal envelopes random distribution. Reveal of qualitative relationships between the temperature increase/decrease measured by thermocouples and the statistical parameters changes are the main result of the paper.

soft tissue phantom, absorption of acoustic energy, temperature marker, signal-to-noise ratio, Nakagami distribution

A B-mode ultrasonography provides structural information on the tissue under investigation encoding the echo strength in gray scale in a two-dimensional image. Interpretation of the B-mode image of breast tissue is done by a physician. The analysis of statistical properties of backscattered RF signal has been recently applied successfully to distinct healthy tissue from tissue lesions regions as a new method of quantitative ultrasound (QUS). Up till now, the most reliable results were obtained for liver and renal tissue lesions, because their normal, healthy structures are nearly homogeneous while a heterogeneous breast tissue classification is still an open issue. The recent study revealed that the medium contraction and expansion induced by a temperature change may cause variations in the relative position of scatterers in a tissue. We have developed a new procedure of heating the patient breast and allowing to observe and record in vivo the influence of temperature changes on a B-mode image and properties of unprocessed radio frequency (RF) backscattered echoes. The initial, feasibility studies of influence of the temperature increase in breast tissue on the intensity, spectrum and statistics of ultrasonic echoes will be discussed.

breast tissue, RF signal, backscattered signal amplitude statistics, spectral properties

Lionel Smith Beale, FRS, (1828–1906), a physician and microscopist in an evocative comparison wrote that the liver resembles a magnificent tree with its trunk and branches, with myriad of leaves, synthesizing and detoxifying. The liver in a human is about the size of football, equipped in a circulatory system and is made of about one million primary lobules which are almost identical, like the leaves of the tree. Therefore, the liver from mathematical point of view can be considered as a micro-periodic medium, and the mathematical methods of homogenisation developed for micro-periodic media can be applied to determine some overall properties of the tissue. Pennes’ equation of heat propagation in biological tissue is a quasi-nonlinear partial differential equation with coefficients depending on temperature T. It consists of three terms, one of which describes Fourier’s heat diffusion, with the diffusion coefficient depending on T. This term is a subject of this contribution.

Pennes’ equation, micro-periodic structure, effective conductivity

For the generation and receiving ultrasonic pulses JSR Ultrasonics DPR 300 Pulser / Receiver and Imasonic Head (center frequency 6MHz, diameter 9 mm, 62 mm focal length) have been used. During the performed experiment three types of phantoms of soft tissue have been used: pure phantom (Phantom A), the second one with glass balls inside with density 6 items per mm3 (Phantom B), the third - 30 balls per mm3 (Phantom C). 10 RF signals were collected for each of the three tissue mimicking phantoms. R interpreter was used, which made automatic import of data, in the packet „wavelet”, reconstruction of signals by Daubechies 6 wavelet family, Multiresolution Analysis i.e. distribution of the different levels of approximations , and at the end the results have been statistically analysed. Histograms and fitting to the Beta and to the normalized and non-normalized Gamma distributions have been performed.
It has been shown that the statistical properties of the signal characteristics include good differentiation between each pattern. They are: the coefficients of non-normalized Gamma distribution in the range of 1-5 levels of approximation, the coefficients of normalized Gamma distribution in the range of 1-7 levels. Beta distributions do not differentiate patterns, as well as higher levels of approximations in the Gamma distributions.

soft tissue phantoms, differentiation of microstructure, backscattered ultrasound, wavelets

For the study of the temperature increase in the soft tissues irradiated by a lowpower ultrasound, see [1], soft tissue phantoms can be used. They should exhibit acoustic properties similar to soft tissue and being sufficiently stable during the hyperthermia treatment. Such phantoms have been produced based on an aqueous solution of agar, oil, and glass microparticles. The FR signals collected in experiments provide to obtain the acoustic properties of phantoms with different numbers of scatterers, from 0-30/mm3. Measured ultrasonic wave velocity in the phantoms is similar to the typical velocity in soft tissues and is equal about 1540 m / s. Attenuation coefficient has been determined by two methods - the pulse method, and the spectral shift method. It is changed in the range of 0.5 to 1.1 dB / (MHz cm), depending on the number of scatterers. It was verified that the patterns do not alter the parameters during 6 months in suitable conditions of storage after production and can be used for further experiments. Besides, based on the analysis of the backscattered signal from pulse/echo ultrasound the statistical properties of the signal envelope and the attenuation coefficient have been studied. It was found that within the total attenuation, the part can be distinguished corresponding to the attenuation due to Rayleigh scattering.

lowpower ultrasound, scatterers number,attenuation, Rayleigh scattering

The behaviour of the interface of a pre-cracked bi-material ceramic - metal structure under static axial loading is an object of interest in the present paper. To solve the problem for an interface de lamination of the structure and to determine the debond length along the interface, own 2D BEM code is created and applied. The interface plate is assumed as a very thin plate comparing with others two. The parametric (geometric and elastic) analysis of the debond length and interface shear stress is done. The obtained numerical results are compared with analytical one from 1D Shear-lag analysis of considered structure. The respective comparison is illustrated in figures and shows a good coincidence.

BEM, Shear-lag analysis, Layered structure