High intensity focused ultrasound (HIFU) has been proven to be promising in non-invasive therapies, in which precise prediction of the focused ultrasound field is crucial for its accurate and safe application. Although the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation has been widely used in the calculation of the nonlinear acoustic field of HIFU, some deviations still exist when it comes to dispersive medium. This problem also exists as an obstacle to the Westervelt model and the Spherical Beam Equation. Considering that the KZK equation is the most prevalent model in HIFU applications due to its accurate and simple simulation algorithms, there is an urgent need to improve its performance in dispersive medium. In this work, a modified KZK (mKZK) equation derived from a fractional order derivative is proposed to calculate the nonlinear acoustic field in a dispersive medium. By correcting the power index in the attenuation term, this model is capable of providing improved prediction accuracy, especially in the axial position of the focal area. Simulation results using the obtained model were further compared with the experimental results from a gel phantom. Good agreements were found, indicating the applicability of the proposed model. The findings of this work will be helpful in making more accurate treatment plans for HIFU therapies, as well as facilitating the application of ultrasound in acoustic hyperthermia therapy.Keywords:KZK equation;fractional order derivative;ultrasound hyperthermia;HIFU;acoustic simulation;Kramers–Kronig relation
Zhizi Ma,Meng Yuan,Ziyong Cheng,Zhuang Yang,Ling Yang,Bin Liu,Yulong Bian,Abdulaziz A. Al Kheraif,Ping'an Ma,Jun Lin
Due to the shallow penetration depth of light in biological tissues, the effectiveness of photothermal therapy (PTT) in deep-seated tumors is limited. Conversely, ultrasonic wave has excellent tissue penetration depth. Using ultrasound (US) as an exogenous physical stimulus to trigger tumors thermotherapy is a promising alternative for deep-seated tumors to supersede conventional PTT. Here, we realized a mild sonothermal therapy (STT) using biodegradable red phosphorus nanoparticles (RP NPs) as sonothermal agents. Quite obvious sonothermal conversion of RP NPs is remarkable under low intensity US irradiation, with the temperature rise from 30 to 47 °C at tumor site. In terms of potential mechanism, under US excitation, the internal electrons of RP NPs undergo transition and release the energy by electrons and holes recombination process. This elicits the atom thermal vibration and raises the temperature around the RP NPs. Additionally, US irradiation can stimulate RP NPs to produce singlet oxygen ( 1 O 2 ) and reduce intracellular energy levels that leads to downregulation of the heat shock proteins (HSPs) expression, providing an “escort” to mild STT. This work offers a new paradigm for the strategies of STT enhanced by sonodynamic effect.
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