Xiaobing Fan

Ultrasound power deposition model for the chest wall.

An ultrasound power deposition model for the chest wall was developed based on secondary-source and plane-wave theories. The anatomic model consisted of a muscle-ribs-lung volume, accounted for wave reflection and refraction at muscle-rib and muscle-lung interfaces, and computed power deposition due to the propagation of both reflected and transmitted waves. Lung tissue was assumed to be air-equivalent. The parts of the theory and numerical program dealing with reflection were experimentally evaluated by comparing simulations with acoustic field measurements using several pertinent reflecting materials. Satisfactory agreement was found. A series of simulations were performed to study the influence of angle of incidence of the beam, frequency, and thickness of muscle tissue overlying the ribs on power deposition distributions that may be expected during superficial ultrasound (US) hyperthermia of chest wall recurrences. Both reflection at major interfaces and attenuation in bone were the determining factors affecting power deposition, the dominance of one vs. the other depending on the angle of incidence of the beam. Sufficient energy is reflected by these interfaces to suggest that improvements in thermal doses to overlying tissues are possible with adequate manipulation of the sound field (advances in ultrasonic heating devices) and prospective treatment planning.

Experimental assessment of power and temperature penetration depth control with a dual frequency ultrasonic system

A novel ultrasound applicator for superficial simultaneous thermoradiotherapy consisting of two parallel-opposed linear arrays and a double-sided scanning reflector was constructed and tested for penetration depth control. In this design the arrays operate at different frequencies (1 and 5 MHz, in this study) and the input power to each array element (five 2 X 2 cm2 elements per array) is computer adjustable. The ultrasonic beams from the arrays are aimed at the scanning reflector which in turn deflects them simultaneously and in parallel toward the treatment volume. Relative intensity distributions generated by the prototype were measured in a degassed water phantom using a thermal technique for a selected reflector position; these showed that the ultrasonic intensity distribution can be controlled in the lateral dimensions by varying the input power level to individual array elements. A fixed-perfused canine kidney phantom was employed to demonstrate experimentally that real time penetration depth control is possible by varying the excitation magnitude of one array (frequency) relative to that of the other. It is concluded that the dual-frequency scanned-reflected ultrasound applicator offers a degree of dynamic three-dimensional control of the power deposition pattern of clinical significance.

Simplified model and measurement of specific absorption rate distribution in a culture flask within a transverse electromagnetic mode exposure system.

In vitro experiments in bioelectromagnetics frequently require the determination of specific absorption rate (SAR) within a layer of cells on the bottom of a culture flask when the SAR has rapid spatial variation both horizontally within the cell layer and vertically in the medium bathing the cells. This problem has only recently been treated in the literature; and it is here approached differently for another irradiation system. It is shown that a simple two-dimensional frequency-domain guided-wave treatment yields results qualitatively comparable to those of more computationally intensive three-dimensional time-domain free-field scattering treatments. The problem of inferring local SARs from temperature-vs.-time curves is shown to be seriously confounded by thermal diffusion; and specific analytic and numerical results are presented to aid in understanding this effect. A novel experimental technique is introduced for measuring millikelvin temperature offsets with subsecond resolution, and illustrative experimental data are presented. Finally, present experimental and theoretical uncertainties are considered; and it is pessimistically asserted that, in a culture flask where spatial SAR variation is rapid, point SAR measurements by thermal methods may be in error by as much as +/- 3 dB. More reliable thermal determinations will require extreme care, challenging technological innovations, or both.

Acoustic field prediction for a single planar continuous-wave source using an equivalent phased array method

Phased array theory is combined with the Rayleigh-Sommerfeld diffraction integral to predict measured acoustic fields generated by a single-source ultrasonic transducer. The idea is to treat a single-source as a phased array, which is composed of many small elements. The goal is to find the excitation source for the phased array, that is, the amplitude and phase for each array element, which produces an acoustic field similar to the experimentally measured field generated by the single-source transducer. A pressure field measured at a given plane parallel and close to the face of the transducer in degased water was used to calculate the excitation source of the equivalent phased array using an inverse technique. The excitation source of the equivalent phased array was then used to calculate the acoustic field from this measurement plane to the far field. It was demonstrated that this phased array approach accurately predicted the location of major grating lobes and the general distributions of the near and far pressure fields for four different transducers. This equivalent phased array method (EPAM) used to model a single-source transducer should be useful in both diagnostic and therapeutic ultrasound applications.

Numerical and in vitro evaluation of temperature fluctuations during reflected-scanned planar ultrasound hyperthermia

Temperature fluctuations inside a target volume during reflected-scanned planar ultrasound hyperthermia were investigated numerically and in vitro. The numerical approach consisted of integrating an ultrasonic power deposition model for a scanning ultrasound reflector linear array system (SURLAS) designed for simultaneous thermoradiotherapy, and a three-dimensional transient version of Pennes bioheat transfer equation. The in vitro approach consisted of delivering hyperthermia to a fixed-perfused canine kidney phantom using a SURLAS prototype. Both approaches allowed the study of temperature fluctuations for several important clinically relevant parameters: scan time, scan distance, perfusion rate and skin cooling. The simulation results showed that the largest temperature fluctuations were located at the opposite ends of the scan window where the scanning reflector comes to a sudden and complete stop and reverses direction. The smallest fluctuations were located at the centre of the scan window. For a given scan distance, the magnitude of the temperature fluctuations increased linearly with increasing scan time, and increased almost linearly as a function of blood perfusion rate. For a scan window of 10 cm x 10 cm and a blood perfusion rate of 5 kg/m3 s, the simulated temperature fluctuations were within +/- 0.5 degree C from the average temperature for scan times less than or equal to 20 s. The in vitro results agreed well with the numerical findings. The measured temperature fluctuations were less than 1.0 degree C for flow rates into the renal artery of less than 200 ml/min and scan times less than 20 s.

An investigation of penetration depth control using parallel opposed ultrasound arrays and a scanning reflector.

A theoretical study of penetration depth control in superficial hyperthermia utilizing parallel opposed linear ultrasound arrays and a double-faced (V-shaped) scanning reflector is presented. This is a dual array system (DAS), where one array operates at a low frequency and the other at a high frequency (1 and 5 MHz, respectively in this study). The arrays are positioned facing each other and both are aimed at a double-faced scanning reflector which distributes the energy over the scanned surface. Each reflecting surface is angled at 45 degrees with respect to the sound propagation direction so that both beams are deflected in the same direction toward the treatment volume. The system was designed to be compatible for combined operation with a medical linear accelerator for the delivery of simultaneous thermoradiotherapy. It is demonstrated that by varying the excitation magnitude of one array relative to the other, it is possible to control the magnitude of absorbed energy as a function of depth, and thus improved control of the heating pattern in all three spatial dimensions is obtained. This improvement is demonstrated with bio-heat transfer simulations which show how penetration depth control translates into control of temperature distributions. The simulations also show that the DAS is able to produce more uniform temperature distributions in highly perfused tissue.

The impact of ultrasonic parameters on chest wall hyperthermia

A transient, three-dimensional acousto-thermal numerical model for chest wall anatomies was developed to evaluate the impact of ultrasonic parameters on thermal coverage. The following independent variables were considered: (1) the relative output intensities of the low and high frequency components of an unfocused dual-frequency ultrasonic beam (xi1); (2) the depths of the soft-tissue bone (d(b)) and soft-tissue-lung (d(u)) interfaces; (3) the intensity reflectivities of these interfaces; and (4) the intensity attenuation coefficient of bone. Several important results were obtained. First, acoustic reflections from the underlying bone and lung surfaces may contribute significantly to heating of the overlying soft-tissue. Secondly, a strong dependence of optimal xi1 values on d(b) and d(u) values was found. Chest wall volumes with 2-3 cm of soft-tissue overlying the ribs were optimal targets for unfocused ultrasound hyperthermia. Thirdly, the maximum steady state temperature in bone also strongly depended on xi1. Finally, the largest difference between the maximum temperature in bone and the maximum temperature in soft-tissue during initial transient heating was between -1.4 degrees C and 0.8 degrees C. That is, the maximum temperature in the field, either during the transient period or at steady state, did not always occur in bone. It is concluded that control of power deposition penetrability offers great potential for improving hyperthermia to chest wall targets in real time.

A concentric-ring equivalent phased array method to model fields of large axisymmetric ultrasound transducers

An equivalent concentric-ring ultrasound phased array method was developed to estimate ultrasonic continuous wave fields generated by axisymmetric single-source transducers. The method models a given source as a concentric-ring phased array by mathematically segmenting it into many rings and subsequently finding the amplitude and phase for each ring that produces an acoustic field similar to the field of the single-source transducer. The excitation source of each ring was calculated using an inverse technique based on complex pressure measurements along a radial line close to the source. The predicting abilities of the method are evaluated by comparing measured and estimated ultrasound fields for six different transducers. The results show that the concentric-ring equivalent phased array method (CREPAM) is able to estimate quantitatively the ultrasound fields generated by large axisymmetric planar and focused transducers.

Ultrasound field estimation method using a secondary source-array numerically constructed from a limited number of pressure measurements

A new and faster method for the accurate estimation of acoustic fields of underwater ultrasonic transducers was developed, tested experimentally, and compared to previously reported methods. Using a limited number of pressure measurements close to the transducers face, the method numerically constructs a virtual secondary source-array whose acoustic field is similar to the field generated by the actual transducer (primary source). The measured data are used to obtain the normal particle velocity on the surface of the virtual secondary source-array, which in turn permits the calculation of the forward propagating field using the Rayleigh-Sommerfeld diffraction integral. The method is novel in that it constructs a virtual secondary source-array, thus eliminating the problems associated with obtaining the excitation source of a real transducer; and it is faster because it uses finite differences instead of a matrix inversion to obtain the excitation source. Results showed that predicted ultrasound fields agreed quantitatively and qualitatively with measured fields for three commonly used transducer types: two planar radiators (one circular, 0.5 MHz, 1.9-cm diam.; and one square, 1 MHz, 1.2 cm on a side), and a sharply focused radiator (1.5 MHz, 10-cm diam., 10-cm radius of curvature). The agreements suggest that the secondary source-array method (SSAM) is applicable to a wide range of radiator sizes, shapes, and operating frequencies. The SSAM was also compared to these authors previous equivalent phased array methods (EPAM) [J. Acoust. Soc. Am. 102, 2734-2741 (1997); and Concentric ring equivalent phased array method (CREPAM), UFFC 46, 830-841 (1999)] which require matrix inversions. The SSAM proved to be much faster and equally or more nearly accurate than the previous methods.

A two-parameter method for the estimation of ultrasound-induced temperature artifacts.

A two-parameter method for the estimation of ultrasound-induced temperature artifacts was evaluated and compared with other commonly applied methods using analytical solutions to the bioheat equation. The two parameters are the exponent of the assumed temperature decay curve after power is turned off and the baseline temperature. These parameters are found by optimizing the fit of the temperature data from 30 to 60s after power is turned off. The artifact is modelled as a point source at the centre of a Gaussian temperature distribution. The blood flow, baseline temperature, and variance of the Gaussian temperature distribution were varied to simulate different clinical situations. Noise was added to the model to investigate the effects of thermometry resolution and sampling intervals. It was found that for artifacts of < 2 degrees C the two-parameter method had errors of less than 0.25 degrees C, whereas other methods generally had greater errors depending on the conduction rate and blood flow rate. The effects of the temperature sampling interval and resolution on the ability of the methods to estimate the artifact were also investigated, and it was found that the two-parameter method was much more sensitive to these parameters than other commonly applied methods.