As a potential non-invasive method of tumor therapy, high intensity focused ultrasound (HIFU) shows great promise with excellent directivity, penetrability and focusing function, which has been used in clinical treatment for solid tumors, such as uterine fibroids and tumors in liver, breast, and prostate.^[1–5] During HIFU therapy, ultrasound in vitro can be focused into the treatment region in the biological tissue, where the temperature could rise to above 65 °C within a short time after absorbing energy, so that the tumors would be induced to irreversible coagulation necrosis without damage to the surrounding tissue.^[6–9]

Despite the uniqueness and remarkable clinical achievements of HIFU, there are still many important scientific problems unresolved, such as treatment program optimization and therapeutic effect evaluation during the treatment process.^[10,11] The heating effect of HIFU on biological tissue is mainly characterized with temperature elevation and tissue lesions, which can be used to adjust treatment programs. The acoustic intensity decreases exponentially as the ultrasound goes deeper into the tissue, and part of the energy would be absorbed by the tissue and converted to heat. The rate of heat change is related to the acoustic intensity and the absorption coefficient of the tissue, while the temperature elevation is subject to tissue absorption, thermal conduction, and blood perfusion. Absolute temperature of the tissue is the leading cause of thermal lesions, but the degree of tissue lesions is determined mostly by the accumulation of heat rather than by absolute temperature. The distribution of temperature elevation and equivalent thermal dose can better characterize the degree of coagulation necrosis in tissue.^[12,13]

When tumors are large enough in diameter, ablation of the entire volume of tumors requires multiple treatment spots administered over a treatment layer by either the ultrasound phased array with electronic scanning or the single source with mechanical scanning.^[14] The ultrasound phased array has many advantages such as multi-focus, no mechanical movement, and short treatment time, but now it is rarely seen in commercial HIFU systems.^[15] On the contrary, mechanical scanning is widely used in clinical therapy, in which the HIFU-sourced transducer or the biological tissue is moved at a certain step size to irradiate each treatment spot for a period of time to realize the superposition of individual treatment spots in terms of the treatment region, resulting in a large tissue lesion in size. However, during scanning therapy, the heating effect of the treatment point will be affected by neighboring treatment spots because of thermal diffusion and dynamic properties, and the consequent changes in temperature elevation and tissue lesions would make the treatment out of control.^[16,17]

It had been proved that tissue property parameters change with temperature variation during HIFU therapy.^[18,19] Clarke et al. found that the increase of attenuation coefficient under ultrasound was due to the irreversible changes in tissue structure, such as protein coagulation.^[20] Zderic et al. validated that the ultrasonic coefficients of liver and spleen tissue after HIFU treatment were about twice as those before HIFU treatment from 1 MHz to 5 MHz.^[21] Some studies have shown that when the temperature rises slowly, the blood vessels would expand and the blood flow velocity would increase to carry away more heat, and the blood perfusion rate would change with the temperature; once the tissue is denatured, the vascular system would collapse and close, and the blood perfusion rate would reduce to 0. The change of tissue properties caused by the heating of HIFU will in turn affect the heating effect of HIFU, including the redistribution of temperature field and the size of tissue lesions.^[22–24] Soneson compared the temperature distribution and the size of the therapeutic area formed under static and dynamic acoustic attenuation ignoring the influence of tissue nonlinearity.^[25]

In this study, an HIFU scanning therapy model with dynamic tissue properties is proposed, and the acoustic fields and temperature fields are solved by finite element method (FEM) to study the influence of tissue properties (i.e., the attenuation coefficient, acoustic velocity, thermal conductivity, specific heat capacity, density, and blood perfusion rate) on temperature elevation and lesions during scanning therapy. The associative influence of thermal diffusion and dynamic tissue properties on temperature distribution and tissue lesions are studied. The results reveal the influence of tissue properties on heating effect during HIFU scanning therapy, providing a reference for the optimization of treatment programs.

An HIFU simulation model is established as shown in Fig. 1, where the ultrasonic transducer is located in the bottom with a focal length of 16 cm and an aperture of 14 cm; there is a hole (diameter: 5 cm) on the center to facilitate the installation of a B-mode ultrasonic probe. The biological tissue, set as a cylinder 4 cm in radius and 6 cm in height, is placed directly above the ultrasonic transducer, and the focus of the ultrasonic transducer corresponds to the geometric center of the tissue. The ultrasonic transducer and tissue are both immersed in water. Acoustic absorbing rubber layer of 5 mm in thickness is set on the left, right, and upper of the model, so ultrasonic waves can be completely absorbed by the boundary to avoid reflections and scatterings. The drive transducer operates at a frequency of 1.391 MHz (all parameters of the transducer refer to PRO2008, Pro hitu, Shenzhen, China). The initial temperature of water and tissue in this model is assumed to be 37 °C, and properties parameters of tissue at this temperature are shown in Table 1.^[26] During scanning therapy, the acoustic pressure near the inner surface of transducer is set to be constant at 0.8 MPa, which is far less than that of cavitation threshold (5.3 MPa).^[27,28] The therapeutic dose remains the same for every treatment spot, and the heating process is completed at one time without interruption. After a treatment spot is heated, the transducer is moved by 4 mm to the next treatment spot along the radial direction of acoustic focus; each movement from one treatment spot to another for 4 mm takes 1 s, when the radiation from transducer is cancelled and heating stops.

Fig. 1.

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	Fig. 1. Geometry of the HIFU model.

Table 1.

Table 1.

Table 1. Properties parameters of tissue at 37 °C. . Material Density/(kg/m3) Acoustic velocity/(m/s) Attenuation coefficient/(Np/m) Specific heat capacity/(J/(kg⋅K)) Thermal Conductivity/(W/(m⋅K)) Blood perfusion rate/(kg/(m3⋅s)) Water 1000 1483 0.025 N/A N/A N/A Tissue 1036 1551 3.5614 3560 0.5212 3.6

Table 1. Properties parameters of tissue at 37 °C. .

Assuming that the acoustic wave propagation is linear and the amplitudes of shear waves in the tissue domain are much smaller than those of the pressure waves, the nonlinear effects and shear waves are therefore neglected,^[3] so the acoustic field can be described by a variable acoustic pressure and then solved by simulation using the approximate Helmholtz wave equation in two-dimensional coordinates as follows:^[26,29]

Here, p is acoustic pressure, ω is the angular frequency, ∇p is acoustic pressure derivative of space, K_z is out-of-plane wave number, while Q_d and q_d are possible unipolar and dipolar source, respectively; K_z, Q_d, and q_d are set to be equal to 0 in this study. The density ρ_c and acoustic velocity c_c are complex-valued to account for properties of medium.

When the plane ultrasonic wave is propagating in the medium, if the acoustic field and intensity field are given, the heat can be calculated by

The temperature elevation in tissue caused by the transformation of acoustic energy into heat can be calculated by Pennes bio-heat transfer equation (BHTE) written as^[32]

According to the Arrhenius equation, the damage rate dΩ/dt can be described as follows:^[33]

In this study, if there are no tissue lesions, the blood perfusion rate can be seen unchanged, otherwise the blood perfusion rate should be defined to be 0. As is shown in Fig. 2, tissue property parameters with temperature are derived from measurements by Damianou, Bamber, Choi, Gunter, et al.,^{[18,22,23,34]} and the expression of property with temperature in tissue is obtained from Fig. 2 through the polynomial approximation method according to the least square theory.^[35] The calculation of temperature and lesions in tissue by finite element method (FEM) can be considered as a nonlinear solving process.^[36] The initial value of acoustic and thermal parameters is shown in Table 1, and the time step length, marked as Δt, is set to be 0.2 s. The spatial grids for the simulation are 0.5 mm. After the distribution of ultrasonic pressure is calculated by Eq. (1) given acoustic parameters, the heat absorbed, obtained based on acoustic attenuation coefficient by Eq. (2), is used to calculate the temperature fields by Eq. (3) combining thermal parameters, and then the temperature can be applied to evaluate tissue lesions by Eq. (5) and generate new acoustic and thermal parameters for next time node calculation according to Fig. 2. The calculation process is shown schematically in Fig. 3.

Fig. 2.

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	Fig. 2. Variations of liver tissue properties with temperatures.

Fig. 3.

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	Fig. 3. Schematic diagram of the computation by FEM.

The heating effect of HIFU on biological tissue is subject to tissue properties. Compared with static tissue properties, the heating effect under dynamic properties presents higher temperature elevation and causes greater tissue lesions. The dynamic change of attenuation coefficient, in comparison of other parameters, has a greater impact on tissue temperature elevation, playing a critical role in influencing temperature elevation among all the tissue properties. During scanning therapy, the temperature elevation on the first treatment spot are much smaller than that on other treatment spots, but the temperature on the last treatment spot drops faster during the cooling period. Besides, the temperature elevation under dynamic properties presents significant growth in comparison to static properties. The shape of ellipsoidal tissue lesion is not symmetrical and the part facing toward the previous treatment spot tends to be larger. Compared with those under static properties, the tissue lesions under dynamic properties, generate with a more unsymmetrical shape and is connected to the tissue lesion around the previous treatment spot. Consequently, all the lesions around four treatment spots are connected with each other to form a closed lesion region. Furthermore, the lesions increase rapidly in size within a few seconds and then begin to level off, but the lesions under dynamic properties begin to appear earlier with larger size, and increase at a faster rate in width. In HIFU clinical therapy, because of the influence of dynamic properties and thermal diffusion, a closed region connected with multiple large lesions is likely to happen, which is also affected by acoustic intensity, movement distance, and heating time, but excessive large size lesions would bring about over treatment and damage to surrounding tissue. On the other hand, differences of temperature elevation and lesion of each treatment spot may cause insufficient treatment around some treatment spots and over treatment around other treatment spots. Therefore, modification and optimization of HIFU treatment programs is necessary to form appropriate uniform lesions, which will guarantee higher efficacy and safety. In this paper, the scanning path is limited to two−dimensional because of the complexity of modeling and calculation, but the results obtained here have guiding significance for clinical application of HIFU.