dr hab. Barbara Gambin 

Doktorat
1979  Fale sprężyste w półprzestrzeni stochastycznie niejednorodnej
 318 
Habilitacja
20080131  Wpływ mikrostruktury na własności kompozytów sprężystych, piezoelektrycznych i termosprężystych  933 
Promotor prac doktorskich
1.  20111124  Mizera Andrzej  Methods for Construction and Analysis of Computational Models in Systems Biology Applications to the Modelling of the Heat Shock Response and the SelfAssembly of Intermediate Filaments  645 
Ostatnie publikacje
1.  Nowicki A., Trawiński Z., Gambin B., Secomski W., Szubielski M.^{♦}, Parol M.^{♦}, Olszewski R., 20MHZ ultrasound for measurements offlowmediated dilation and shear rate in the radialartery, ULTRASOUND IN MEDICINE AND BIOLOGY, ISSN: 03015629, DOI: 10.1016/j.ultrasmedbio.2018.02.011, Vol.44, No.6, pp.11871197, 2018 Streszczenie: A highfrequency scanning system consisting of a 20MHz linear array transducer combined with a 20MHz pulsed Dopplerprobe was introduced to evaluate the degree of radial artery ﬂowmediated 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. (Email: anowicki@ippt.gov.pl) © 2018 World Federation for Ultrasound in Medicine & Biology. All rights reserved. Słowa kluczowe: Flowmediated vasodilation, Radial artery, Shear rate, Reactive hyperemia, Endothelium, Pulsed doppler, Ultrasonography Afiliacje autorów:
 35p.  
2.  Wójcik J., Gambin B., Theoretical and numerical aspects of nonlinear reflection–transmission phenomena in acoustics, Applied Mathematical Modelling, ISSN: 0307904X, DOI: 10.1016/j.apm.2016.10.026, Vol.42, pp.100113, 2017 Streszczenie: Equations of nonlinear acoustic wave motion in a nonclassical lossy medium are used to derive generalised formulas describing the phenomena of reflection and transmission. Integral, nonlocal 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, onedimensional 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. Słowa kluczowe: Nonlinear sound wave, Nonlinear reflection, Nonclassical absorption, Soft tissues Afiliacje autorów:
 35p.  
3.  Byra M., Kruglenko E., Gambin B., Nowicki A., Temperature Monitoring during Focused Ultrasound Treatment by Means of the Homodyned K Distribution, ACTA PHYSICA POLONICA A, ISSN: 05874246, DOI: 10.12693/APhysPolA.131.1525, Vol.131, No.6, pp.15251528, 2017 Streszczenie: 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 Słowa kluczowe: Temperature monitoring, homodyned K distribution, focused ultrasound Afiliacje autorów:
 15p.  
4.  Karwat P., Kujawska T., Lewin P.A.^{♦}, Secomski W., Gambin B., Litniewski J., Determining temperature distribution in tissue in the focal plane of the high (>100 W/cm2) intensity focused ultrasound beam using phase shift of ultrasound echoes, Ultrasonics, ISSN: 0041624X, DOI: 10.1016/j.ultras.2015.10.002, Vol.65, pp.211219, 2016 Streszczenie: 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 thermoablative 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 echosignals received by an ultrasound scanner from this very volume is presented. To improve spatial resolution of Bmode 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 tissuemimicking 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 algorithmdetermined 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 contrasttonoise ratio of 3.5–12 dB in the temperature range 21–56°C. Concurrently performed, conventional Bmode 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 MRIguided temperature imaging for prediction of the location and extent of the thermal lesion prior to applying the final HIFU treatment. Słowa kluczowe: Ultrasonic temperature imaging, HIFU, Echo phase shift, Velocity image contrast Afiliacje autorów:
 30p.  
5.  Gambin B., Byra M., Kruglenko E., Doubrovina O.^{♦}, Nowicki A., Ultrasonic Measurement of Temperature Rise in Breast Cyst and in Neighbouring Tissues as a Method of Tissue Differentiation, ARCHIVES OF ACOUSTICS, ISSN: 01375075, DOI: 10.1515/aoa20160076, Vol.41, No.4, pp.791798, 2016 Streszczenie: 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. Słowa kluczowe: medical ultrasound, temperature changes in vivo, breast tissue, ultrasonic temperature measurement Afiliacje autorów:
 15p.  
6.  Gambin B., Kruglenko E., Byra M., Relationships between Acoustical Properties and Stiffness of Soft Tissue Phantoms, HYDROACOUSTICS, ISSN: 16421817, Vol.19, pp.111120, 2016 Streszczenie: Polyvinylalcohol cryogel is commonly used for soft tissue phantom manufacture. The gel formation from an aqueous solution of polyvinylalcohol 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. Słowa kluczowe: soft tissue phantoms, elastography, ultrasound attenuation, speed of sound, Nakagami maps, stiffness Afiliacje autorów:
 6p.  
7.  Karwat P., Kujawska T., Secomski W., Gambin B., Litniewski J., Application of ultrasound to noninvasive imaging of temperature distribution induced in tissue, HYDROACOUSTICS, ISSN: 16421817, Vol.19, pp.219228, 2016 Streszczenie: 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 thermoablative 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 echosignals 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. Słowa kluczowe: HIFU, echo phase shift, parametric imaging, velocity/brightness CNR Afiliacje autorów:
 6p.  
8.  Gambin B., Wójcik J., Doubrovina O.^{♦}, Differentiation of random structure properties using wavelet analysis of backscattered ultrasound, HYDROACOUSTICS, ISSN: 16421817, Vol.19, pp.121128, 2016 Streszczenie: 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. Słowa kluczowe: spectrogram, scalogram, wavelets, random scattering structure Afiliacje autorów:
 6p.  
9.  Ivanova J.^{♦}, Nikolova G.^{♦}, Becker W.^{♦}, Gambin B., Interface behavior of a bimaterial plate under dynamic loading. Cohesive interface debonding, ZAMMZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 00442267, DOI: 10.1002/zamm.201300119, Vol.95, No.11, pp.11901201, 2015 Streszczenie: The paper deals with the elastic and cohesive interface behavior of precracked bimaterial ceramicmetal 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 bimaterial structure, assuming the cohesive interface behaviour, accompanied before of the elasticbrittle 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 bimaterial 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 bimaterial 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 ceramicmetal composites on metal substrates and is depicted in figures. Słowa kluczowe: Dynamic behaviour of bimaterial structure, cracked plate, shear lag model, elasticbrittle and cohesive interface delamination, debond length Afiliacje autorów:
 25p.  
10.  Gambin B., Kruglenko E., Temperature Measurement by Statistical Parameters of Ultrasound Signal Backscattered from Tissue Samples, ACTA PHYSICA POLONICA A, ISSN: 05874246, DOI: 10.12693/APhysPolA.128.A72, Vol.128, No.1A, pp.A7278, 2015 Streszczenie: A novel estimation of temperature changes inside soft tissues has been proposed in subablation range, i.e. 20°C48°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 Kdistribution. 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 Kdistribution 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. Słowa kluczowe: therapeutic applications, ultrasonics, medical imaging Afiliacje autorów:
 15p.  
11.  Gambin B., Kruglenko E., Gałka A.A.^{♦}, Wojnar R., Macroscopic thermal properties of quasilinear cellular medium on example of the liver tissue, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 22993649, Vol.22, No.4, pp.329346, 2015 Streszczenie: 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. Słowa kluczowe: heat transport, asymptotic homogenisation, effective heat conductivity Afiliacje autorów:
 14p.  
12.  Byra M., Gambin B., Temperature detection based on nonparametric statistics of ultrasound echoes, HYDROACOUSTICS, ISSN: 16421817, Vol.18, pp.1723, 2015 Streszczenie: 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 KulbackLeiber 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. Słowa kluczowe: ultrasoud echoes, noninvasive temperaturę monitoring, Kolmogorov Smirnov distance, KulbackLeiber divergence Afiliacje autorów:
 6p.  
13.  Gambin B., Kruglenko E., Wójcik J., Relationship between thermal and ultrasound fields in breast tissue in vivo, HYDROACOUSTICS, ISSN: 16421817, Vol.18, pp.5358, 2015 Streszczenie: 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 nonuniform 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. Słowa kluczowe: temperature field, backscattered ultrasonic signals, breast tissue in vivo, FEM model Afiliacje autorów:
 6p.  
14.  Wójcik J., Gambin B., Litniewski J., Theoretical results and numerical study on the nonlinear reflection and transmission of plane sound waves, HYDROACOUSTICS, ISSN: 16421817, Vol.18, pp.181192, 2015 Streszczenie: 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 Słowa kluczowe: Nonliear reflection, transmission, Riccati equation Afiliacje autorów:
 6p.  
15.  Nowicki A., Gambin B., Ultrasonic Synthetic Apertures: Review, ARCHIVES OF ACOUSTICS, ISSN: 01375075, DOI: 10.2478/aoa20140047, Vol.39, No.4, pp.427438, 2014 Streszczenie: 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. Słowa kluczowe: synthetic aperture, effective aperture, ultrasonography Afiliacje autorów:
 15p.  
16.  Doubrovina O.^{♦}, Gambin B., Kruglenko E., Temperature level and properties of wavelet approximations of back scattered ultrasound, HYDROACOUSTICS, ISSN: 16421817, Vol.17, pp.3746, 2014 Streszczenie: 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. Słowa kluczowe: ultrasound echoes, soft tissue sample in vitro, statistical marker of temperaturę rise Afiliacje autorów:
 7p.  
17.  Kruglenko E., Gambin B., RF signal amplitude statistics during temperature changes in tissue phantoms, HYDROACOUSTICS, ISSN: 16421817, Vol.17, pp.115122, 2014 Streszczenie: Two heating protocols for soft tissue phantoms have been performed. An AgarGelOil (AGO) mixture has been heated locally by applying ultrasonic beams and a Poly Vinyl Alcoholcryogel (PVAc) 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 Kdistributed random variables for AGO and PVAc, respectively. Temperature is linked to the scale parameter of Rayleigh distribution for the AGO, and the shape parameter of Kdistribution for PVAc were calculated and discussed in the context of their suitability for the acoustic measurement of temperature. Słowa kluczowe: AgarGel_Oil soft tissue phantom, Kdistribution shape parameter, temperaturę measurements Afiliacje autorów:
 7p.  
18.  Gambin B., Bielski W.^{♦}, Incompressible limit for a magnetostrictive energy functional, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 02397528, DOI: 10.2478/bpasts20130110, Vol.61, No.4, pp.320326, 2013 Streszczenie: The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and nonlocal 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 nonlocal elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ convergence. The nonlocality is limited to nonlocal elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional. Słowa kluczowe: gammaconvergence, incompressibility, magnetostrictive material, second gradient of deformation, existence of minimizers Afiliacje autorów:
 25p.  
19.  Kruglenko E., Gambin B., Cieślik L., Soft TissueMimicking Materials With Various Number of Scatterers and Their Acoustical Characteristics, HYDROACOUSTICS, ISSN: 16421817, Vol.16, pp.121128, 2013 Streszczenie: For the study of the temperature increase in the soft tissues irradiated by a lowpower ultrasound [1], soft tissuemimicking 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 semitransmission 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. Słowa kluczowe: acoustical characteristics, soft tissue mimicking material, scatterers number Afiliacje autorów:
 7p.  
20.  Gambin B., Doubrovina O.^{♦}, Statistical properties of wavelet transform coefficients of backscattering signal from soft tissues and their phantoms, HYDROACOUSTICS, ISSN: 16421817, Vol.16, pp.5966, 2013 Streszczenie: 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. Słowa kluczowe: backscattered RF signals , skin cancer differentiation, scatterers numer, wavelet approximations Afiliacje autorów:
 7p.  
21.  Ivanova J.^{♦}, Nikolova G.^{♦}, Gambin B., Interface delamination of bimaterial structure under time harmonic load. Cohesive behaviour of the interface, ZAMMZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 00442267, DOI: 10.1002/zamm.201000210, Vol.92, No.1, pp.4151, 2012 Streszczenie: The interface cohesive behaviour and interface delamination in a bimaterial structure consisting of two plates and material interface with zero thickness under time harmonic load is studied. Previously, the authors studied the elastobrittle interface behaviour, from both sides of a crack, initially normal to the interface, when the elasticbrittle 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 elasticbrittle 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 elastobrittle 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 ceramicmetal composite on metal substrate. The influence of frequencies and amplitude fluctuations on the cohesive debond length and the interface shear stress distribution are discussed. Słowa kluczowe: dynamic behaviour of bimaterial structure, cracked plate, shear lag model, Laplace transform, cohesive interface delamination, cohesive debond length Afiliacje autorów:
 20p.  
22.  Mizera A., Gambin B., Modelling of ultrasound therapeutic heating and numerical study of the dynamics of the induced heat shock response, COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, ISSN: 10075704, DOI: 10.1016/j.cnsns.2010.04.056, Vol.16, No.5, pp.23422349, 2011 Streszczenie: 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 timecourse profile is composed with the temperaturedependent 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. Słowa kluczowe: Hyperthermia, Heat Shock Response dynamics, Ultrasound therapeutic treatment, mathematical modelling Afiliacje autorów:
 40p.  
23.  Gambin B., Ivanova J.^{♦}, Valeva V.^{♦}, Nikolova G.^{♦}, Precracking and interfacial delamination in a bimaterial structure: Static and dynamic loadings, ACTA MECHANICA SINICA, ISSN: 05677718, DOI: 10.1007/s1040901104143, Vol.27, No.1, pp.8089, 2011 Streszczenie: The behavior of a precracked bimaterial structure interface under given static and dynamic axial loading is an interest object in the present paper. Firstly, it is shown that the shearlag model is a proper tool to analyze a delamination process in a precracked bimaterial structure undergoing static loading. Secondly, the “shearlag 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 shearlag model together with the Laplace transforms and halfanalytical 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 shearlag 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 ceramicmetal composite, namely cermet, and depicted in figures. Słowa kluczowe: Debond length, Precracked bimaterial structure, Shearlag model, Delamination, BEM Afiliacje autorów:
 25p.  
24.  Ivanova J.^{♦}, Nikolova G.^{♦}, Gambin B., Interface delamination of bimaterial structure under dynamic time harmonic loading, ZAMMZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN: 00442267, DOI: 10.1002/zamm.200900369, Vol.91, No.2, pp.146154, 2011 Streszczenie: The interface behaviour between two layers of 2D elastic structure under dynamic timeharmonic load is studied. The “shear lag model” is adopted and applied to the dynamic response of bimaterial structure, assuming the elasticbrittle behaviour of the interface. The Laplace transforms together with halfanalytical 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 ceramicmetal 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. Słowa kluczowe: Dynamic behaviour of bimaterial structure, cracked plate, shear lag model, elasticbrittle interface delamination, debond length Afiliacje autorów:
 20p.  
25.  Gambin B., Kruglenko E., Kujawska T., Michajłow M., Modeling of tissues in vivo heating induced by exposure to therapeutic ultrasound, ACTA PHYSICA POLONICA A, ISSN: 05874246, Vol.119, pp.950956, 2011 Streszczenie: 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 threelayer 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 twophase 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. Słowa kluczowe: focused ultrasound, soft tissues, local thermal fields, numerical modelling Afiliacje autorów:
 15p.  
26.  Valeva V.^{♦}, Ivanova J.^{♦}, Gambin B., BEM and Shear lag method for interface problem of bimaterial structure under static loading, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 14292955, Vol.41, No.9, pp.1729, 2011 Streszczenie: The behaviour of the interface of a precracked bimaterial ceramicmetal 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 elasticbrittle debond lengths with Song's experimental data for the bimaterial structure Zinc/Steel as well as with respective results from FEM simulation shows good coincidence. Słowa kluczowe: BEM, Shear lag analysis, bimaterial structure, debond length Afiliacje autorów:
 15p.  
27.  Kruglenko E., Gambin B., Some aspects of numerical modeling of temperature increase due to ultrasound beam irradiation of rat liver, HYDROACOUSTICS, ISSN: 16421817, Vol.14, pp.99110, 2011 Streszczenie: 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. Afiliacje autorów:
 4p.  
28.  Wójcik J., Litniewski J., Nowicki A., Gambin B., Applying crystallography in analysis of trabecular bone backscatter, HYDROACOUSTICS, ISSN: 16421817, Vol.14, pp.255266, 2011 Streszczenie: Some important details of the Backscatter Effective CrossSections (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. Słowa kluczowe: Multi scattering, Random structures Afiliacje autorów:
 4p.  
29.  Mizera A., Gambin B., Stochastic modeling of the eukaryotic heat shock response, JOURNAL OF THEORETICAL BIOLOGY, ISSN: 00225193, DOI: 10.1016/j.jtbi.2010.04.029, Vol.265, No.3, pp.455466, 2010 Streszczenie: 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 farreaching ramifications for the cell biology. Słowa kluczowe: Stochastic model, Computer simulations, Markov chain, Gillespie algorithm, Stationary distribution Afiliacje autorów:
 32p.  
30.  Bielski W.^{♦}, Gambin B., Relationship between existence of energy minimizers of incompressible and nearly incompressible magnetostrictive materials, REPORTS ON MATHEMATICAL PHYSICS, ISSN: 00344877, Vol.66, No.2, pp.147157, 2010 Streszczenie: 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. Słowa kluczowe: micromagnetics, magnetostrictive material, incompressible, nearly incompressible materials, existence problem Afiliacje autorów:
 13p.  
31.  Gambin B., Kujawska T., Kruglenko E., Mizera A., Nowicki A., Temperature fields induced by low power focused ultrasound during gene therapy. Numerical predictions and experimental results, ARCHIVES OF ACOUSTICS, ISSN: 01375075, Vol.34, No.4, pp.445460, 2009 Streszczenie: 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. Słowa kluczowe: heatresponsive gene therapy, temperature field, lowpower focused ultrasound, soft tissues, ultrasonic regime control, heat sources distribution, heat shock proteins Afiliacje autorów:
 9p.  
32.  Gambin B., Gałka A.^{♦}, Telega J.J., Tokarzewski S., Influence of anisotropy induced by microcracks on effective elastic properties, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867888X, Vol.53, No.4, pp.409420, 2005  
33.  Gambin B., Trzęsowski A., Probabilistyczne przestrzenie metryczne, Prace IPPT  IFTR Reports, ISSN: 22993657, No.60, pp.148, 1972 
Lista ostatnich monografii
1. 118  Gambin B., Wpływ mikrostruktury na własności kompozytów sprężystych, piezoelektrycznych i termosprężystych, Rozprawa habilitacyjna, IPPT Reports on Fundamental Technological Research, 12, pp.1183, 2006 
Lista rozdziałów w ostatnich monografiach
1. 572  Doubrovina O.^{♦}, Tymkiewicz R., PiotrzkowskaWróblewska H., Gambin B., Aktualności Inżynierii Akustycznej i Biomedycznej, rozdział: Linking of structural parameters to properties of ultrasound backscattered signals by the threads phantoms study, Polskie Towarzystwo Akustyczne, Oddział w Krakowie, I, pp.6779, 2018  
2. 573  Gambin B., Kruglenko E., Litniewski J., Tymkiewicz R., Aktualności Inżynierii Akustycznej i Biomedycznej, rozdział: Dynamic elasticity, acoustical impedance and attenuation of special tissuelike phantoms, Polskie Towarzystwo Akustyczne, Oddział w Krakowie, I, pp.8996, 2018  
3. 574  Korczak I., Gambin B., Kruglenko E., Aktualności Inżynierii Akustycznej i Biomedycznej, rozdział: Stabilizacja temperatury organu podczas zabiegu transplantacji, Polskie Towarzystwo Akustyczne, Oddział w Krakowie, I, pp.97103, 2018  
4. 575  Kruglenko E., Korczak I., Gambin B., Aktualności Inżynierii Akustycznej i Biomedycznej, rozdział: Efektywność hipertermii ultradźwiękowej w agarowych wzorcach tkanki miękkiej domieszkowanych różnymi składnikami, Polskie Towarzystwo Akustyczne, Oddział w Krakowie, I, pp.105113, 2018  
5. 576  Drozd J.^{♦}, Gambin B., Aktualności Inżynierii Akustycznej i Biomedycznej, rozdział: Solidification of dental material Clearfil F2 described by composite rheological model, Polskie Towarzystwo Akustyczne, Oddział w Krakowie, I, pp.8187, 2018  
6. 489  Gambin B., Kruglenko E., Byra M., Postępy Akustyki, rozdział: Pomiary zmian temperatury we wzorcach tkanki miękkiej przez termopary i wstecznie rozproszone sygnały ultradźwiękowe, Polskie Towarzystwo Akustyczne, Oddział Warszawski, Warszawa, Poland, 1, pp.1526, 2016  
7. 495  Litniewski J., Klimonda Z., Karwat P., PiotrzkowskaWróblewska H., DobruchSobczak K., Tymkiewicz R., Gambin B., Postępy Akustyki 2016, rozdział: Cancer malignancy sonic markers, Polskie Towarzystwo Akustyczne, Oddział Warszawski, Warszawa, Poland, pp.4960, 2016  
8. 424  Wójcik J., Gambin B., Dynamical Systems. Mathematical and Numerical Approaches, rozdział: Numerical analysis of reflection and transmission phenomena of nonlinear ultrasound wave, Wydawnictwo Politechniki Łódzkiej, Awrejcewicz, M. Kaźmierczak, J. Mrozowski, P. Olejnik (Eds.), pp.603614, 2015  
9. 348  Gambin B., Doubrovina O.^{♦}, Complex Analysis and Potential Theory with Applications, rozdział: Wavelet analysis for temperature increase detection from acoustic backscattered signal, Cambridge Scientific Publishers, T. Aliev Azerogly, A. Golberg, S.V. Rogosin (Eds.), pp.6376, 2014  
10. 16  Gambin B., Lekszycki T., Kowalczyk T., Kowalewski T.A., Ziółkowski A., Pieczyska E.A., Stupkiewicz S., Scenariusze rozwoju technologii nowoczesnych materiałów metalicznych, ceramicznych i kompozytowych, rozdział: Biomateriały. Rola i strategia badawcza IPPT PAN w powstaniu nowoczesnych technologii materiałów współpracujących z ludzkimi tkankami, Wydawnictwo Naukowe Instytutu Technologii Eksploatacji PIB, 1, pp.181222, 2010  
11. 17  Gambin B., Scenariusze rozwoju technologii nowoczesnych materiałów metalicznych, ceramicznych i kompozytowych, rozdział: Biomateriały. Strategia i projekt działań wspomagających tworzenie w Warszawie interdyscyplinarnego klastra naukowców z lekarzami i firmami działającymi na rzecz medycyny, Wydawnictwo Naukowe Instytutu Technologii Eksploatacji PIB, 1, pp.230242, 2010  
12. 18  Gambin B., Scenariusze rozwoju technologii nowoczesnych materiałów metalicznych, ceramicznych i kompozytowych, rozdział: Biomateriały. Uwagi o strategii rozwoju technologii biomateriałów współpracujących z ludzkimi tkankami w Polsce, Wydawnictwo Naukowe Instytutu Technologii Eksploatacji PIB, 1, pp.243251, 2010  
13. 19  Gambin B., Scenariusze rozwoju technologii nowoczesnych materiałów metalicznych, ceramicznych i kompozytowych, rozdział: Biomateriały. Scenariusze rozwoju technologii biomateriałów w Polsce na podstawie matematycznej analizy krzyżowej, Wydawnictwo Naukowe Instytutu Technologii Eksploatacji PIB, 2, pp.174184, 2010  
14. 219  Kruglenko E., Gambin B., Bielski W.R.^{♦}, Elektromagnetyczne techniki w ochronie zdrowia, rozdział: Materiały nieściśliwe magnetosprężyste jako model tkanek z mikromagnetycznymi cząstkami, CIOP PIB (Warszawa), Krawczyk A., Duraj A. (Eds.), pp.96109, 2007  
15. 179  Bielski W.^{♦}, Gambin B., Kruglenko E., Nonsmooth/Nonconvex Mechanics with applications in Engineering II. NNMAE206, A volume dedicated to the memory of Professor P.D.Panagiotopoulos, rozdział: Selected problems of rigid and deformable micromagnetics, ZITI, Baniotopoulos C.C. (Ed.), pp.6976, 2006  
16. 213  Gałka A.^{♦}, Gambin B., Kruglenko E., Bioelektromagnetyzm: teoria i praktyka, rozdział: Zagadnienie minimalizacji w analizie mikromagnetyków nieodkształcalnych, CIOPPIB (Warszawa), Krawczyk A., Zyss T. (Eds.), 6, pp.101119, 2006 
Prace konferencyjne
1.  Kruglenko E., Korczak I., Litniewski J., Gambin B., Ultrasound Thermal Effect Enriched by Adding of Micro and Nano Particles to the AgarGel Tissue Mimicking Materials, IEEE 2018, IEEE Joint Conference  Acoustics, 20180911/0914, Ustka (PL), DOI: 10.1109/ACOUSTICS.2018.8502361, No.1, pp.158163, 2018 Streszczenie: Agargel based materials are widely used as tissue mimicking materials. Pure agargel is stable up to 60◦C but exhibits small ultrasound attenuation compared to a soft tissue. To enhance the attenuation of agargel we fabricated samples of agargel with the adding of graphite micro particles (GMP), magnetic micro particles (MMP) and magnetic nano particles (MNP) with two weight fractions of dry powders added before the formation of the gel to the aqueous agar solution, namely 0.8 % and 1.6 %, respectively. In order to compare the thermal effect caused by the addition of a particles, the samples immersed in a water bath were heated by 2 MHz circular focused transducer (diameter 44 mm), with power of 1, 2, 3 and 4 W. The temperature rise curves were recorded using thermocouples. The temperature change rate (TCR) in the initial point of heating was calculated. For the 0.8 % weight fraction the MMP sample had the highest TCR value at each sound power tested, the smallest value had the MNP sample. For the 1.6 % weight fraction, the highest TCR value had the MNP sample, while the smallest TCR had the GMP sample. We stated that for the higher fraction of particles, the MNP material had the highest TCR value for all powers, and besides the difference between TCR in MMP and GMP samples was less than the difference between TCR in MMP and MNP samples. Besides, the MNP sample exhibited the minimal exposure time to achieve the temperature increment of 5◦C for all applied acoustic powers. These facts underline the unique properties of MNP material and its usefulness as a model material for ultrasonic hyperthermia experiments. Słowa kluczowe: tissue mimicking materials, ultrasound hyperthermia, nano and micro magnetic particles, temperature change rate Afiliacje autorów:
 
2.  Nowicki A., Trawiński Z., Gambin B., Secomski W., Szubielski M.^{♦}, Parol M.^{♦}, Olszewski R., Measurements of Flow Mediated Dilation and Shear Rate in the Radial Artery Using 20 MHz Ultrasonic System in Patients with Coronary Artery Disease., XXI Międzynarodowy Kongres Polskiego Towarzystwa Kardiologicznego, 20170921/0923, Katowice (PL), pp.1, 2017 Streszczenie: A novel highfrequency scanning system, with a 20MHz linear array transducer combined with 20MHz pulsed Doppler, was introduced to evaluate the degree of radial artery flowmediated 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 ± 4.835·104 in group I and 1.3 ± 0.89·104 in group II. Statistically significant differences between the two groups were confirmed by WilcoxonMannWhitney test for FMD and FMD/SR (pvalues < 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. Słowa kluczowe: flow mediated vasodilation, radial artery, shear rate, reactive hyporaemia, endothelium, pulsed Doppler, ultrasonography. Afiliacje autorów:
 
3.  Nowicki A., Piotrzkowska H., DobruchSobczak K., Litniewski J., Byra M., Gambin B., Kruglenko E., Differentiation of normal tissue and tissue lesions using statistical properties of backscattered ultrasound in breast, IUS 2015, IEEE International Ultrasonics Symposium, 20151021/1024, Taipei (TW), DOI: 10.1109/ULTSYM.2015.0417, pp.P1B6154, 2015 Streszczenie: 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 echosignal and Bmode 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 cutoff) plus Nakagami statistics showed 100% of sensitivity with specificity equal 57.33%, decreasing the number of lesions which were biopsied from 34 to 28. Słowa kluczowe: breast cancer, quantitative ultrasound, BIRADS Afiliacje autorów:
 
4.  Piotrzkowska H., Nowicki A., Litniewski J., Gambin B., DobruchSobczak K.^{♦}, Breast carcinoma tissues characterization using statistics of ultrasonic backscatter, FA2014, 7th FORUM ACUSTICUM 2014, 20140907/0912, Kraków (PL), No.SS27_7, pp.19, 2014 Streszczenie: 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%. Słowa kluczowe: quantitative ultrasound, breast cancer, statistics Afiliacje autorów:
 
5.  Doubrovina O.^{♦}, Litniewski J., Gambin B., Wavelet approximations and statistical approach to random fluctuations of amplitude in backscattered ultrasonic signal, FA2014, 7th FORUM ACUSTICUM 2014, 20140907/0912, Kraków (PL), No.SS27_2, pp.16, 2014 Streszczenie: 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 (PVAC, the prefreezing 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 lowpass filter what qualitatively improved the temperature estimating. The latter was realized by observing the variations of the shape parameter of Kdistribution. 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. Słowa kluczowe: random signals, Polyvinyl Alcohol – Cryogel, wavelet approximation, temperaturę monitoring Afiliacje autorów:
 
6.  Kruglenko E., Gambin B., Statistical analysis of ultrasonic signals backscattered from heated tissue phantom and soft tissue samples in vitro, FA2014, 7th FORUM ACUSTICUM 2014, 20140907/0912, Kraków (PL), No.SS27_3, pp.19, 2014 Streszczenie: 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 Kdistribution 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 Kdistribution is the best statistical marker of a temperature level in the performed experiments. Słowa kluczowe: therapeutic applications, ultrasonics, medical imaging Afiliacje autorów:
 
7.  Karwat P., Litniewski J., Secomski W., Kujawska T., Krawczyk K., Kruglenko E., Gambin B., Nowicki A., Nieinwazyjne obrazowanie temperatury tkanki miękkiej in vitro metodą analizy przemieszczenia ech ultradźwiękowych, 59th Open Seminar on Acoustics, 20120910/0914, Boszkowo (PL), pp.101104, 2012 Streszczenie: 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. Słowa kluczowe: obrazowanie temperatury, prędkość akustyczna Afiliacje autorów:
 
8.  Kruglenko E., Mizera A., Gambin B., Tymkiewicz R., Zienkiewicz B., Litniewski J., Nagrzewanie ultradźwiękami tkanek miękkich in vitro i własności akustyczne wytworzonych wzorców tkanek miękkich, 59th Open Seminar on Acoustics, 20120910/0914, Boszkowo (PL), pp.129132, 2012 Streszczenie: 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. Słowa kluczowe: wzorce tkanek, sygnał ultradźwiękowy, prędkość dźwięku, tłumienie, statystyka rozproszenia Afiliacje autorów:
 
9.  Gambin B., Doubrovina O.^{♦}, Wavelet approach to RF signal analysis for structural characterization of soft tissue phantom, 59th Open Seminar on Acoustics, 20120910/0914, Boszkowo (PL), pp.6972, 2012  
10.  Karwat P., Litniewski J., Secomski W., Kujawska T., Krawczyk K., Kruglenko E., Gambin B., Noninvasive imaging of thermal fields induced in soft tissues in vitro by focused ultrasound using analysis of ultrasonic echoes displacement, International Conference Biomedical Engineering, 20121025/1026, Kaunas (LT), pp.6672, 2012 Streszczenie: 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 noninvasive imaging ultrasound technique. Słowa kluczowe: HIFU, therapeutic ultrasound, ultrasonic imaging, echo strain estimation Afiliacje autorów:
 
11.  Kruglenko E., Gambin B., Modelowanie numeryczne obszaru nagrzewania oraz intensywności źródła ciepła w szczurzej wątróbce in vivo naświetlanej skoncentrowaną wiązką ultradźwiękową o niskiej mocy, 57 Otwarte Seminarium z Akustyki, 20100920/0924, Gliwice (PL), pp.103106, 2010 Streszczenie: 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. Afiliacje autorów:

Abstrakty konferencyjne
1.  Gambin B., Kruglenko E., Byra M., Acoustical Properties of Tissue Phantoms with Different Stiffness and WaterLike Absorption, 10th EAA International Symposium on Hydroacoustics, 20160517/0516, Jastrzębia Góra (PL), DOI: 10.1515/aoa20160038, pp.361, 2016 Streszczenie: Poly(vinyl alcohol) cryogel, PVAC, is produced as a soft tissuemimicking material, suitable for application in ultrasound imaging. A 10% by weight poly(vinyl alcohol) in water solution was used to form PVAC, 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 PVAC produced by 1, 2 and 3 cycles of freezingthawing 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? Słowa kluczowe: soft tissue phantoms, elastography, ultrasound attenuation, speed of sound, Nakagami maps, stiffness Afiliacje autorów:
 
2.  Doubrovina O.^{♦}, Gambin B., Wójcik J., Detection of Variations in Random Characteristics of Scattering Medium by the Wavelet Analysis, 10th EAA International Symposium on Hydroacoustics, 20160517/0516, Jastrzębia Góra (PL), DOI: 10.1515/aoa20160038, No.2, pp.360, 2016  
3.  Gambin B., Kruglenko E., Byra M., Thermocouple measurement of temperature variations in soft tissue phantoms versus backscattered ultrasonic signals properties, OSA 16, LXIII Otwarte Seminarium z Akustyki, 20160913/0916, Białowieża (PL), DOI: 10.1515/aoa20160059, pp.617, 2016 Słowa kluczowe: soft tissue phantoms, backscattered ultrasonic signal, changes in the backscattered energy Afiliacje autorów:
 
4.  Litniewski J., Klimonda Z., Karwat P., PiotrzkowskaWróblewska H., DobruchSobczak K., Tymkiewicz R., Gambin B., Cancer Malignancy Sonic Markers, OSA 16, LXIII Otwarte Seminarium z Akustyki, 20160913/0916, Białowieża (PL), DOI: 10.1515/aoa20160059, No.3, pp.622, 2016  
5.  Gambin B., Byra M., Doubrovina O.^{♦}, Nonparametric statistics indirect temperature estimation by ultrasound imaging, 8th International Scientific Seminar on Analytic Methods of Analysis and Differential Equations, 20150914/0918, Mińsk (BY), Vol.1, pp.26, 2015 Streszczenie: 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 twodimensional matrix. These data are divided according to the regions of interest (ROI) analyzed piecewise in the following way: Słowa kluczowe: temperaturę detection, nonparametric statistics, backscattered ultrasound, wavelet Afiliacje autorów:
 
6.  Nowicki A., DobruchSobczak K., Piotrzkowska H., Litniewski J., Gambin B., Roszkowska K.^{♦}, Chrapowicki E.^{♦}, Clinical Validation of the Statistical Analysis of US RF Signals in Differentiation of the Breast Lesions, AIUM 2015, Ultrasound in Medicine and Biology Annual Convention, 20150321/0325, Lake Buena Vista (US), DOI: 10.1016/j.ultrasmedbio.2014.12.403, Vol.41, No.4S, Special issue: 2015 AIUM Annual Convention and Preconvention Program Hosting WFUMB Congress, ABSTRACT 2088809, pp.S98S99, 2015 Streszczenie: 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. Słowa kluczowe: breast cancer, ultrasound, RF echosignal Afiliacje autorów:
 
7.  Wójcik J., Gambin B., Numerical analysis of reflection and transmission phenomena of nonlinear ultrasound wave, DSTA 2015, 13th Conference on DYNAMICAL SYSTEMSTheory and Applications, 20151207/1210, Łódź (PL), pp.603, 2015 Streszczenie: Numerical analysis of the reflection/transmission problem for a nonlinear 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. Słowa kluczowe: Nonliear reflection, transmission, Riccati equation, Numerical caslculations Afiliacje autorów:
 
8.  Gambin B., Kruglenko E., Wojnar R., Macroscopic thermal properties of quasilinear cellular medium on example of the liver tissue, NHT 2015, Numerical Heat Transfer 2015 – Eurotherm Seminar No. 109, 20150927/0930, Warszawa (PL), pp.177178, 2015 Streszczenie: 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 microperiodic cellular medium, and in circumstances justified by biological reasons, the mathematical methods of homogenisation developed for microperiodic 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 oxygenrich 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. Słowa kluczowe: liver tissue, Pennes’ equation, heat transport, asymptotic homogenization, effective coefficients Afiliacje autorów:
 
9.  Gambin B., Kruglenko E., Secomski W., Karwat P., Temperature dependencies of ultrasound signals backscattered from an agaroil softtissue mimicking material, PCMCMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 20150908/0911, Gdańsk (PL), pp.215216, 2015 Streszczenie: Tissue mimicking materials for ultrasound research, phantoms, should be acousticaly similar to the tissues. Such requirements are filled by the AGO (agaroil) 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. Słowa kluczowe: soft tissue phantom, absorption of acoustic energy, temperature marker, signaltonoise ratio, Nakagami distribution Afiliacje autorów:
 
10.  Gambin B., Kruglenko E., Byra M., Nowicki A., Piotrzkowska H., DobruchSobczak K., Changes in ultrasound echoes of a breast tissue in vivo after exposure to heat  a case study, PCMCMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 20150908/0911, Gdańsk (PL), pp.217218, 2015 Streszczenie: A Bmode ultrasonography provides structural information on the tissue under investigation encoding the echo strength in gray scale in a twodimensional image. Interpretation of the Bmode 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 Bmode 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. Słowa kluczowe: breast tissue, RF signal, backscattered signal amplitude statistics, spectral properties Afiliacje autorów:
 
11.  Wojnar R., Gambin B., Thermal properties of biomaterials on the example of the liver, PCMCMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 20150908/0911, Gdańsk (PL), pp.267268, 2015 Streszczenie: 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 microperiodic medium, and the mathematical methods of homogenisation developed for microperiodic media can be applied to determine some overall properties of the tissue. Pennes’ equation of heat propagation in biological tissue is a quasinonlinear 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. Słowa kluczowe: Pennes’ equation, microperiodic structure, effective conductivity Afiliacje autorów:
 
12.  Gambin B., Doubrovina O.^{♦}, Analiza wstecznie rozproszonego sygnału ultradźwiękowego we wzorcach tkankowych z wykorzystaniem statystyki współczynników transformaty falkowej, XX Conference on Acoustic and Biomedical Engineering, 20130415/0419, Zakopane (PL), pp.3940, 2013 Streszczenie: 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 nonnormalized Gamma distributions have been performed. Słowa kluczowe: soft tissue phantoms, differentiation of microstructure, backscattered ultrasound, wavelets Afiliacje autorów:
 
13.  Kruglenko E., Gambin B., Cieślik L., Soft tissue phantoms and backscattered signal analysis to determine their acoustical properties, XX Conference on Acoustic and Biomedical Engineering, 20130415/0419, Zakopane (PL), pp.3738, 2013 Streszczenie: 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 030/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. Słowa kluczowe: lowpower ultrasound, scatterers number,attenuation, Rayleigh scattering Afiliacje autorów:
 
14.  Bielski W.^{♦}, Gambin B., An estimation of wave velocities in geomaterials, SolMech 2010, 37th Solid Mechanics Conference, 20100906/0910, Warszawa (PL), pp.240241, 2010  
15.  Gambin B., Tokarzewski S., Ivanova J.^{♦}, Bounds on strength tensor for piezoelectric composites, SolMech 2010, 37th Solid Mechanics Conference, 20100906/0910, Warszawa (PL), pp.3233, 2010  
16.  Gambin B., Kruglenko E., Kujawska T., Modelowanie procesu nagrzewania tkanek in vivo wywołanego terapeutycznymi ultradźwiękami, XVII Konferencja Inzynierii Akustycznej i Biomedycznej, 20100322/0326, Zakopane (PL), pp.8889, 2010  
17.  Veleva V.^{♦}, Ivanova J.^{♦}, Gambin B., BEM for interface problem of bimaterial structure under static loading, 11th National Congress on Theoretical and Applied Mechanics, 20070902/0905, Borovets (BG), Vol.CD ROM, pp.16, 2009 Streszczenie: The behaviour of the interface of a precracked bimaterial 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 Shearlag analysis of considered structure. The respective comparison is illustrated in figures and shows a good coincidence. Słowa kluczowe: BEM, Shearlag analysis, Layered structure Afiliacje autorów:
 
18.  Ivanova J.^{♦}, Nikolova G.^{♦}, Gambin B., Interface delamination of bimaterial structure under dynamic loading, 11th National Congress on Theoretical and Applied Mechanics, 20070902/0905, Borovets (BG), Vol.CD ROM, 2009 