Quadratic versus linear models to estimate the mean scattering spacing as a function of temperature in ex-vivo tissue.

Previous works have shown the feasibility of temperature estimation during ultrasonic therapy using pulse-echo diagnostic ultrasound. These methods are based on the measurement of thermally induced changes in backscattered RF echoes due to thermal expansion and changes in ultrasonic velocity. They assume a joint contribution of these two parameters and a linear dependence with temperature. In this work, the contributions of velocity changes and thermal expansion to the evolution of the mean scatterer spacing of ex vivo bovine skeletal muscle tissue samples were decoupled. This was achieved by employing an experimental setup which allows measuring the absolute velocity value, using the through-transmission technique in a direct transmission configuration. The mean-scatterer spacing was estimated from spectral analysis of the backscattered signals obtained in pulse-echo mode. We propose a quadratic model of the thermal expansion coefficient to fit the evolution of the mean-scatterer spacing with temperature. The temperature increase estimated by the linear model, in the range of 29.5-47 °C, presents a percentage error (mean square error) of 11 %, while for the quadratic model the error is 4.8 %.

Durability study of a gellan gum-based tissue-mimicking phantom for ultrasonic thermal therapy.

Stability and duration of ultrasonic phantoms are still subjects of research. This work presents a tissue-mimicking material (TMM) to evaluate high-intensity therapeutic ultrasound (HITU) devices, composed of gellan gum (matrix), microparticles (scatterers), and chemicals. The ultrasonic velocity and attenuation coefficient were characterized as a function of temperature (range 20 °C-85 °C). The nonlinear parameter B/A was determined by the finite amplitude insertion substitution (FAIS) method, and the shear modulus was determined by a transient elastography technique. The thermal conductivity and specific heat were determined by the line source method. The attenuation was stable for 60 days, and in an almost linear frequency dependence (0.51f0.96 dB cm-1), at 20 °C (1-10 MHz). All other evaluated physical parameters are also close to typical soft tissue values. Longitudinal ultrasonic velocities were between 1.49 and 1.75 mm µs-1, the B/A parameter was 7.8 at 30 °C, and Young's modulus was 23.4 kPa. The thermal conductivity and specific heat values were 0.7 W(m K)-1 and 4.7 kJ(kg K)-1, respectively. Consistent temperature increases and thermal doses occurred under identical HITU exposures. Low cost, longevity, thermal stability, and thermal repeatability make TMM an excellent material for ultrasonic thermal applications. The TMM developed has the potential to assess the efficacy of hyperthermia devices and could be used to adjust the ultrasonic emission of HITU devices.

Ex vivo determined experimental correction factor for the ultrasonic source term in the bioheat equation.

The objective of this work is to propose an effective absorption coefficient (αeffec) as an empirical correction factor in the source term of the bioheat equation. The temperature rise in biological tissue due to ultrasound insonification is produced by energy absorption. Usually, the ultrasonic absorption coefficient (αA) is used as a source term in the bioheat equation to quantify the temperature rise, and the effect of scattering is disregarded. The coefficient αeffec includes the scattering contribution as an additional absorption term and should allow us to make a better estimation of the thermal dose (TD), which is important for clinical applications. We simulated the bioheat equation with the source term considering αA or αeffec, and with heating provided by therapeutic ultrasound (1MHz, 2.0Wcm-2) for about 5.5min (temperature range 36-46°C). Experimental data were obtained in similar heating conditions for a bovine muscle tissue (ex vivo) and temperature curves were measured for depths 7, 30, 35, 40 and 45mm. The TD values from the experimental temperature curves at each depth were compared with the numerical solution of the bioheat equation with the classical and corrected source terms. The highest percentual difference between simulated and experimental TD was 42.5% when assuming the classical αA, and 8.7% for the corrected αeffec. The results show that the effective absorption coefficient is a feasible parameter to improve the classical bioheat transfer model, especially for depths larger than the mean free propagation path.

Influence of ultrasonic scattering in the calculation of thermal dose in ex-vivo bovine muscular tissues.

This study explores the effect of ultrasound scattering on the temperature increase in phantoms and in samples of ex-vivo biological tissue through the calculation of the thermal dose (TD). Phantoms with different weight percentages of graphite powder (0-1%w/w, different scattering mean free paths, ℓS) and ex-vivo bovine muscle tissue were isonified by therapeutic ultrasound (1 MHz). The TD values were calculated from the first 4 min of experimental temperature curves obtained at several depths and were compared with those acquired from the numerical solution of the bio-heat transfer equation (simulated with 1 MHz and 0.5-2.0 W cm(-2)). The temperature curves suggested that scattering had an important role because the temperature increments were found to be higher for higher percentages of graphite powder (lower ℓS). For example, at a 30-mm depth and a 4-min therapeutic ultrasound application (0.5 W cm(-2)), the TDs (in equivalent minutes at 43 °C) were 7.2, 17.8, and 58.3 for the phantom with ℓS of 4.35, 3.85, and 3.03 mm, respectively. In tissue, the inclusion of only absorption or full attenuation in the bio-heat transfer equation (BHTE) heat source term of the simulation leads to under- or overestimation of the TD, respectively, as compared to the TD calculated from experimental data. The experiments with phantoms (with different scatterer concentrations) and ex-vivo samples show that the high values of TD were caused by the increase of energy absorption due to the lengthening of the propagation path caused by the changing in the propagation regime.

Application of the Schlieren pulsed method for the observation of simple and multiple scattering of ultrasonic waves.

The Schlieren pulsed method uses short-term lighting triggered by an acoustic pulse. This allows for an observation of elastic deformation fields in pulsed regime and for an evaluation of the evolution of the pulse in the interior of homogenous and heterogeneous media. In this paper we apply the Schlieren pulsed method to determine the conditions of the change from simple to multiple scattering. An ultrasound transducer put in water emits a wide-band pulse. The pulse goes through a region of parallel cylindrical wires, uniformly spaced and perpendicular to the acoustic beam. Varying the width of the zone of the scatterer cylinders, it is possible to optically observe the transmitted acoustic field and to calculate the transmission coefficient. By studying the behavior of this coefficient in function of the medium width, we obtained the zone in which the transition between simple and multiple scattering happens.