Mqa.ogpta.polsl.plMolecular and Quantum Acoustics vol. 28 (2007) ULTRASONIC PARAMETERS OF HEN'S EGG
Krzysztof J. OPIELINSKI Institute of Telecommunications, Teleinformatics and Acoustics, Wroclaw University of Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, POLAND Hen's egg is an easily accessible biomolecular model for ultrasonic study. It is a perfect object, allowing testing of the visualization possibilities by means of ultrasound transmission tomography. The aim of paper is showing complex characteristics of the ultrasonic parameters of hen's egg in the frequency range 1–10 MHz. Keywords: ultrasonic parameters, ultrasound transmission tomography, hen's egg, white, yolk The increase in the use of ultrasonic waves for medical purposes creates the need for continuous research in the field of ultrasonic characteristics of various biological media. Thorough quantitative analysis of ultrasonic parameters of biological tissues is difficult due to the complex structure and variety of constituents such as proteins and lipids. Albumens containing amino acids can be found in all living organisms, including both animals and plants. They are the main constituents of those organisms and are the basic building material of tissues. Hen's egg is an easily accessible biomolecular model for ultrasonic study. The process of transformation of sol into gel in case of hen's egg white is currently being studied by means of many various methods (viscosity measurements, electrophoresis, light scattering, chemical analyses ); ultrasonic wave propagation velocity and attenuation measurements during coagulation and denaturation process is one of the best measurement methods . Additionally, transparent polyacrylamide (PAM) gels containing hen's egg white perfectly imitate electric and thermal characteristics of human tissues. Consequently, as phantom material they are of great importance for the development of hyperthermia and warming therapies such as HIFU (high intensity focused ultrasound) . Due to its oval shape Opieliński K.J. (transmission of ultrasonic wave possible from many angles around it), structure and acoustic parameters (relatively little attenuation and slight refraction of ultrasonic wave beam on water-white-yolk boarders), a boiled hen's egg with removed shell is a perfect model, allowing testing of the possibilities of biological structures visualization by means of ultrasonic projection (UP) and ultrasonic transmission tomography (UTT) methods [4,5,6]. Hen's egg white, as a typical, easily accessible and natural protein substance, is a useful study subject for biomedical engineers and food technologists [7,8,9]. A lot of studies are related to food industry. The subjects of research include dried, frozen and liquid ingredients acquired from hen's eggs, which are used in the process of preparing various food products (confectionery, ice cream, sauces). Additionally, literature offers detailed studies related to processes of qualification, cleaning and removing egg shell, filtering, mixing, coagulation, foaming, emulsifying as well as pasteurization and freezing or dehydrating (the primary purpose of pasteurization of liquid egg ingredients is killing bacteria) . It is, however, difficult to find a publication providing comprehensive characteristics of ultrasonic parameters of hen's egg (especially in the area of 1 – 10 MHz frequencies used in ultrasonic transmission tomography). The aim of this study is to provide those characteristics.
2. HEN'S EGG STRUCTURE Fig.1 shows hen's egg structure [11,12]. The most important part of an egg is yolk (also called yolk sphere) with a germinal disk. Yolk is the biggest known oocyte produced by vertebrates. Egg yolk has heterogeneous structure and consists of concentrically arranged layers, of which two are the most important: white and yellow yolk. They are divided by yolk membranes (3 – 10 μm) made of keratin and mucin . White yolk fills the centre of the yolk sac and stretches to germinal disk, which contains a nucleus. During development the germinal disk undergoes segmentations (cleavage) and transforms into a germ. The yellow yolk is an energy source and a building material for cells. Yolk contains proteins, fats and carbohydrates. Yolk is agglomerated in a given place in an egg, and is protected by a vitelline yolk membrane (12 – 23 μm) .
Molecular and Quantum Acoustics vol. 28 (2007) Fig. 1. Hen's egg structure: a) structure, b) picture.
The yolk sphere is surrounded by egg white. Egg white consists of 3 layers: outer thin, inner thick and inner thin, all of which surround the yolk. The outer liquid layer is located under shell membrane consisting of two closely adherent membranes (thickness: outer 30 – 36 μm, inner 40 – 48 μm), which separate towards the rounded end of the egg creating an air cell . The central dense part of egg white consists of thick spiral bands, called chalazas, the function of which is to attach the yolk sphere to the soft lining membrane and keep it in central position during egg rotation. As a result yolk can only rotate around the long axis of the egg. The whole egg is protected form the outside by a stiff shell, mostly made of calcium carbonate. There are many pores in the shell, allowing oxygen to reach the inside of the egg and carbon dioxide, which is a by-product of the germ's life processes, to be released outside. The shell is covered with cuticule, the main chemical constituents of which are mucin and some unspecified glycoproteids capable of protecting the egg against microorganisms. The cuticule surrounding the pores is an important means of protection both in terms of mechanical and chemical hazards. The estimated average composition of hen's egg is as follows: 59% white, 30% yolk, 10% shell, 1 % membranes.
The size of hen's egg is about 4.5 x 6 cm and the weight is about 50 – 70 g. Egg yolk and white consist of water, proteins, lipids, carbohydrates and nonorganic constituents (Tab.1). Yolk contains about 33% of lipids and 49% of water. 99% of white is water and proteins. The constitution is the main reason for the differences in ultrasonic parameter values of yolk and white.
Opieliński K.J. Tab. 1. Chemical constitution of hen's egg yolk and white .
Percentage in yolk [%] Percentage in white [%] minute quantities nonorganic constituents The primary types of proteins in hen's egg white are ovalbumin, ovotransferrin, conalbumin, ovomucoid, lysozyme, globulins and ovomucin [12,15]. The largest part of egg yolk proteins are lipoproteins . One of the components of lipids is cholesterol. A big hen's egg, with 17 g yolk, contains around 213 mg of cholesterol . White and yolk density is nearly the same (1035 kg/m3) . It is difficult to determine the exact physical and chemical properties of hen's eggs due to variability of the measured parameters predominantly resulting from individual differences  and aging of biological material. Hen's egg aging process results most importantly in reduction of the amount of white's thick layer (Fig.1) and degradation of yolk vitelline membrane endurance [7,8].
3. ULTRASONIC PARAMETERS Studies by Carstensen and other researchers , related to blood constituents and measurements of its acoustic parameters suggest that propagation velocity and ultrasonic wave attenuation in water protein solutions depend primarily on proteins concentration. In temperature range of 10 – 40 °C for every gram of proteins in 100 cm3 of solution sound velocity increases around 4 m/s in comparison to sound velocity in pure water , and maximum velocity dispersion in frequency range of 0.3 – 10 MHz is about 0.6 m/s for every 11.4 g of proteins in 100 cm3 of solution . If hen's egg white is treated as a water solution containing 10 g of proteins in 100 cm3 of solution, sound velocity should be about 40 m/s higher than sound velocity in water. This was confirmed in measurements performed by Javanaud and others . The values of ultrasonic wave propagation velocity in hen's egg white (thin layer) in temperature function were calculated in this study using fifth order polynomial, the coefficients of which were adjusted to the 13 measurement values achieved by Takagi, Choi and Bae : egg _ white = ∑ i where t is temperature in the range of 0 – 100 °C, and ki are coefficients specified in Tab.2. Relation (1) was presented by means of a graph in Fig.2.
Molecular and Quantum Acoustics vol. 28 (2007) Tab. 2. Equation coefficients (1).
According to research by Akashi, Kushibiki and Dunn , ultrasonic wave propagation velocity value in thick (middle) layer of hen's egg white is higher than velocity value in thin outer by around 4 – 15 m/s. Sound velocity dispersion in white thick layer occurs in the range from a few to e few hundred MHz and is insignificant (0.0019 m/s/MHz). In the thin outer layer it does not occur [7,20]. Hen's egg aging process results in reduction of sound velocity value in both white and yolk by about 10 – 20 m/s . Transverse waves can also propagate in hen's egg white, but these, as in the case of tissues (e.g. pig fat αT ≈ 526713 dB/m/MHz), are severely attenuated . Transverse wave velocity in hen's egg white estimated for 2.5 MHz frequency is about 4 m/s .
Attenuation coefficient in water protein solutions is a linear function of their concentration, up to 15 g for 100 cm3 . The mechanism of ultrasonic waves attenuation in protein solutions is complex and cannot be described by means of a single molecular relaxation process . Despite the differences in rheological properties of the thick and thin layer of hen's egg white, ultrasonic wave attenuation coefficient values do not vary . Choi, Bae and Takagi  suggested a formula allowing determining ultrasonic wave attenuation values in hen's egg white. The formula was modified for the purposes of this study in order to enable determining the attenuation values in [dB/m]: = k ⋅ f [dB / m] , egg _ white where f is the frequency of the propagated wave in [MHz], kt – coefficient dependent on temperature in [dB/m/MHz1.25]. A similar relation (with 1.2 exponent) is true for blood [17, 22], which suggests that the relaxation mechanism occurring in hen's egg white, that consists of a few types of proteins is similar to the mechanism occurring in single protein (ovalbumin) solution. Ultrasound attenuation coefficient values changes in hen's egg white resulting from egg's aging processes were not observed .
Fig.2 presents a graph of ultrasonic wave propagation velocity in hen's egg white (thin layer) in temperature function, calculated using fifth order polynomial (1), the coefficients of which were adjusted to the 13 measurement values achieved by Takagi, Choi and Bae  (the measurement values are marked) – curve 1, in relation to sound velocity in water Opieliński K.J. calculated using polynomial presented by Marczak  – curve 2 and coefficient kt = α/f 1.25 in relation to temperature for hen's egg white (the measurement values obtained during the study  are marked) – curve 3. Comparatively, ultrasonic wave attenuation coefficient in water for 1 MHz frequency in temperature range of 0 – 80 °C decreases from 0.5 to 0.07 dB/m .
Hen's egg yolk, which consists of 30 % of fat and 50 % of water, can be treated as emulsion with 16 % of proteins. Coefficient of ultrasonic wave attenuation in yolk is reduced when temperature rises and becomes higher when frequency rises . Similar acoustic parameters changes were observed during studies on polystyrene spheres suspended in water performed by Allegra and Hawley . Sound velocity dispersion in yolk occurs only at frequencies above several tens of MHz. Its value is about 0.065 m/s/MHz [7,20]. Sound velocity in yolk is around 20 m/s lower than it is in white .
Fig. 2. Relation of sound velocity in hen's egg white (thin layer) in temperature function, calculated using formula (1) – curve 1, sound velocity in water in temperature function calculated using polynomial presented by Marczak  – curve 2, ultrasonic wave attenuation coefficient α/f 1.25 = kt [dB/m/MHz1.25] in relation to temperature for hen's egg white (the measurement values obtained during the study  are marked) – curve 3.
Measurements show, that the value of ultrasonic wave attenuation in yolk can be determined by means of the following relation: = k ⋅ f [dB / m] , egg _ yolk where f is the frequency of the propagated wave in [MHz], k 't– coefficient dependent on temperature . Using experimental data from the study , coefficient k ' Molecular and Quantum Acoustics vol. 28 (2007) [dB/m/MHz1.5] was determined for the temperature of 20 °C (Fig.3a). Ultrasonic wave attenuation in relation to temperature in yolk has been shown for three frequency values, based on experimental data taken from the study  (Fig.3b).
a) Fig. 3. Ultrasonic wave attenuation in hen's egg yolk: a) in relation to frequency: curve – values calculated for t = 20 °C using formula (3), triangles – values measured by Javanaud, Rahalkar and Richmond , b) in relation to temperature – on the basis of the measurements in the study .
It is difficult to find information about studies related to nonlinear B/A parameter for hen's egg white and yolk. Liu and others  give the following values: B/A = 3.7 for white and B/A = 5 for yolk. According to studies performed by Ballou  in liquids, there is a linear relation between B/A parameter and ultrasonic wave propagation velocity reciprocal. Later, two relations were shown (theoretical and empirical), which allow calculation of nonlinear B/A parameter for liquids : B / A = 2 + 9800 / c , B / A = − 5 0 +1200 / c .
Errabolu, Sehgal, Bahn and Greenleaf showed that similar relations are also true for tissues, especially those containing fat : B / A = 89570 / c − t = 20 C B / A = 62500 / c − t = 30 C B / A = 50120 / c − t = 37 C However, calculations performed for white and yolk using the above formulas give higher values than those presented in scientific literature.
Ultrasonic parameters of a raw and boiled hen's egg white and yolk, measured for 2 MHz frequency, in the temperature of 20 °C, are shown in table 3 [6,7,9,19,20].
Opieliński K.J. Tab. 3. Ultrasonic parameters of a raw and boiled hen's egg white and yolk, measured for 2 MHz frequency, in the temperature of 20 °C.
ρ [kg/m3] Z [kg/(m2∙s)] ∙ 106 1507■ (21.5°C) 1504 - 1510■○ ■ – , – , ○ – , □ – , ♦ -  4. TEMPERATURE HYSTERESIS EFFECT Hen's egg white's spatial structure changes under the influence of temperature . Transformation of sol into gel occurs (coagulation process). These changes are reversible as long as denaturation has not occurred (egg white sets) as a result of temperatures in the range of 62 – 65 °C. Raw egg white is transparent, because protein molecules are bound in bundles. Rising temperature causes the protein bundles to unwind, and separate protein molecules begin cling together. As a result a random net of protein strands is formed, the egg white becomes jellied and looses its transparency. During the denaturation process hydrogen bonds and which give protein molecules their specific shape, are destroyed. The curve for sound velocity in relation to temperature in white is similar in terms of shape to the curve for water. The proteins forming the white solution in water result in the curve shifting towards lower temperatures and higher sound velocity values. On the basis of the graph shown in fig.2 (curve 3) it is possible to conclude that ultrasonic wave attenuation for hen's egg white lowers when temperature rises (similar to protein or other molecule solutions ) until temperature value of about 58 °C, at which egg white coagulation and denaturation process begins. After this point attenuation rises with temperature until 62 °C is reached, then attenuation value is constant until the temperature of about 65 °C. Finally, attenuation value starts rising again [2,19].
The transformation of white into gel results in reduction of ultrasonic wave velocity  and increase of ultrasonic wave attenuation . In case of sol relation of ultrasonic wave velocity and attenuation to temperature in egg white is reversible. After the temperature, at which transformation process of sol into gel begins is exceeded (58 – 60 °C), a phenomenon of temperature hysteresis of ultrasonic parameters in white occurs [2,19] (Fig.4). Despite the hysteresis loops being not closed the phenomenon can be called hysteresis because all the characteristic features of it defined in Wielka Encyklopedia PWN are present : „hysteresis (Greek: hysteresis – lack, shortage) – physical relation of parameters change (characteristic Molecular and Quantum Acoustics vol. 28 (2007) for a system state or properties), caused by a change in external factors, to system history (i.e. states preceding a given state)" [translation of original definition in Polish].
Fig. 4. The phenomenon of temperature hysteresis in hen's egg white: a) for ultrasonic wave velocity , b) for ultrasonic wave attenuation .
After the temperature, at which transformation process of sol into gel begins is exceeded (Fig.4, point 2), the position of temperature curves for ultrasound velocity and attenuation in white depends on the maximum temperature of the gel (Fig.4, points 4,6,8). For example, after egg white is heated up to the maximum temperature of t = 65 °C (curves 1–2-4), ultrasound velocity and attenuation are related to temperature as visible on curves 4-5. Temperature hysteresis effect in gel means that density of the protein net, which was formed during heating up to a specific temperature remains stabile while cooling down and reheating. Because the net's density is related to maximum temperature the temperature curves of ultrasound velocity and attenuation in hen's egg white change only when the maximum temperature of white heating is increased. This means that the values of ultrasounds velocity and attenuation in hen's egg white depend on its thermal history. Additionally, hen's egg white is characterised by significant inertia; a sudden rise in temperature results in a slow reduction of ultrasonic wave velocity value and a slow rise of ultrasonic wave attenuation value, until saturation value is reached after about 90 minutes [2,19]. This inertia is caused by a process of slow formation of protein net.
Hen's egg yolk sets at a temperature about 5 °C higher than in case of white (65 –70 °C). This is due to the protein molecules being bound to fat molecules in yolk. More energy is needed in case of yolk in order for proteins to separate from fat molecules; only after this occurs, denaturation similar to the one taking place in egg white structure is possible.
Opieliński K.J. 5. MEASUREMENTS AND CALCULATIONS On the basis of previously performed ultrasonic transmission measurements of a boiled hen's egg with a removed shell  (time of flight and receiving pulse amplitude were measured among other values), average values (projections) were determined for velocity cp(x)׀z=0 and attenuation of ultrasonic wave αp(x)׀z=0 for a longitudinal cross-section of an egg (Fig.5a), which was submerged in a tank filled with water (the temperature was t = 24°C), which was used as a coupling medium. The measurements were taken using two ultrasonic transmitting-receiving probes, which had 5 MHz operating frequency, 5 mm diameter and were mechanically adjusted (1.5 mm step). The distance between the probes submerged in water was l = 10 cm. The measured value of sound velocity in water was cp = cw = 1493.74 ± 0.12 m/s, and the ultrasonic wave attenuation value was αp = αw = 4.9065 ± 0.05 dB/m. The reconstruction of the average sound velocities in white cegg_white was performed in area A of the longitudinal section of the egg (Fig.5a) on the basis of formula: legg _ white egg _ white where legg_white – ultrasonic wave path in egg white, lw - ultrasonic wave path in water (l = lw + legg_white in area A), cp – projection of ultrasonic wave velocity on path l. Values legg_white were determined on the basis of an optical image of the egg cross-section in the location of the measurements (Fig.5a), with uncertainty of around ± 0.25 mm. The average values of sound velocity in egg white, reconstructed on the basis of formula (9), (with numerically determined reconstruction uncertainty of about ± 5 m/s) are shown in Fig.5b; the average value calculated from the three values (shaded area) is cegg_white = 1529.71 m/s (Tab.4).
Similarly, the reconstruction of the average values of ultrasonic wave attenuation in white αegg_white was performed in area B of the longitudinal cross-section of the egg (Fig.5a) on the basis of formula: egg _ white legg _ white where Uw = 1528.71 mV – pulse amplitude received after transmission through water on path l, Up – pulse amplitude received after transmission through water and egg. Receiving pulse amplitude measurement uncertainty was around ± 5 mV. The average values of ultrasonic wave attenuation in hen's egg white, reconstructed on the basis of formula (10), (with numerically determined reconstruction uncertainty of about ± 5 dB/m) are shown in Fig.5b; Molecular and Quantum Acoustics vol. 28 (2007) the average value calculated from the three values (shaded area) is αegg_white = 202.18 dB/m (Tab.4).
On the basis of formula: legg _ yolk egg _ yolk egg _ white egg _ white where legg_yolk - ultrasonic wave path in yolk on the basis of an optical image of the egg cross-section in the location of the measurements, in area C (Fig.5a), with uncertainty of around ± 0.25 mm (l = lw+legg_white+legg_yolk), cegg_white = 1530 ± 5 m/s, the local values of sound velocity in hen's egg yolk were reconstructed in a similar way (with numerically determined reconstruction uncertainty of about ± 5 m/s) – Fig.5c; the average value calculated from the three values (shaded area) is cegg_yolk = 1501.42 m/s (Tab.4).
Similarly, the reconstruction of the local values of ultrasonic wave attenuation in yolk αegg_yolk (with numerically determined reconstruction uncertainty of about ± 50 dB/m) was performed in area C of the longitudinal section of the egg (Fig.5a) on the basis of formula: egg _ white egg _ yolk ) egg _ white egg _ white egg _ yolk legg _ yolk where αegg_white = 202 ± 50 dB/m. The average value calculated from the three values (shaded area in Fig.5c) is αegg_yolk = 924.99 dB/m (Tab.4).
Tab. 4. Ultrasonic parameters of a boiled hen's egg white and yolk reconstructed on the basis of projection measurements for the temperature of 24 °C.
αegg_white αegg_yolk αegg_yolk [dB/m] αegg_yolk [dB/m] Opieliński K.J. Fig. 5. Determination of ultrasonic wave velocity and attenuation in the white and yolk of a boiled hen's egg with removed shell: a) optical image of the measured cross-section with projection of velocity and attenuation values, b) average values of velocity and attenuation in white reconstructed from projection, c) average values of velocity and attenuation in yolk reconstructed from projection.
In the study the structure, chemical constitution and some physical properties of hen's egg were described. The characteristics of chosen ultrasonic parameters of egg white and yolk (density, ultrasonic wave velocity and attenuation, acoustic impedance, nonlinear B/A parameter), measured and calculated in frequency range of 1 – 10 MHz and used for internal structure of biological object visualisations by means of UP and UTT methods were also shown.
On the basis of measurements data an empirical equation, allowing determining of sound velocity in hen's egg white in temperature function was developed.
Analysis of measurements presented in literature it was discovered that as a result of the occurrence of the phenomenon of temperature hysteresis in hen's egg white and yolk, in the Molecular and Quantum Acoustics vol. 28 (2007) case of ultrasonic parameters of boiled hen's eggs used as objects for testing the possibilities of biological structures visualization there is a certain variation of values related to their thermal history, which for sound velocity in white is about 5 m/s and for ultrasonic wave attenuation in white is about 20 dB/m/MHz1.25.
The values reconstructed from projection measurements of a boiled and shell-less hen's egg submerged in water were as anticipated.
It is worth noting that the presented measurements and calculations are characterised by a certain range of variability related to chemical constitution and physical properties of hen's eggs originating from various breeding, individual differences and aging of biological material. Hen's egg aging process results most importantly in reduction of the amount of white's thick layer and degradation of yolk vitelline membrane endurance [7,8], which causes predominantly reduction of sound velocity value in both white and yolk by about 10 – 20 m/s.
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A spatial econometric model for productivity and innovation in the manufacturing industry: the role played by geographical and sectorial distances between firms° Ilaria Sangalli*, Marco Lamieri** Abstract The paper assesses spillovers from total factor productivity (TFP) in the Italian
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