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The focused ultrasound pressure fields inevitably exhibit nonlinear effects, which can influence the ablation region. However, the nonlinear effects exhibit noticeable variations across different applications. The characterization of the nonlinear pressure fields of ultrasound is important for the effective implementation of focused ultrasound therapy.<\/jats:p><\/jats:sec><jats:sec><jats:title>Purpose<\/jats:title><jats:p>The traditional angular spectrum method (ASM) was extended to accurately and efficiently simulate the propagation of weakly nonlinear ultrasound in heterogeneous mediums of clinical model. The nonlinear effects were further analyzed in relationship to the transducer parameters that are different in various applications.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>The pressure fields were simulated using the extended ASM, incorporating calculations for phase aberration in the frequency domain and magnitude compensation in the spatial domain to account for heterogeneous acoustic impedance mismatch. Validation was performed by comparison to k\u2010Wave simulation results using two simplified clinical models, an abdominal soft tissue and a transcranial skull model. The nonlinear effects were then analyzed in relation to the transducer parameters of f\u2010number and effective source area based on the same acoustic output power. The analysis of nonlinear effects was conducted under both homogeneous medium and the clinical models.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>The simulation results demonstrated a maximum error of 3.93% in the calculated harmonic pressure of the abdominal model, and a maximum error of 4.89% within the transcranial model when comparing the extended ASM simulation results to those obtained from k\u2010Wave simulations. The characterization of the nonlinear effects reveals a strong correlation with the transducer parameters. Specifically, the results indicate that the nonlinear effects intensify with an increase in the effective source area and f\u2010number, under the same acoustic output power of the transducer. However, the clinical model also showed an influence on the nonlinear effects in relation to the f\u2010number.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>The extended ASM was demonstrated as an accurate and efficient simulation tool, and the simulation results provide a reference for evaluating the intensity of nonlinear effects in various transducer designs.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.17270","type":"journal-article","created":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T16:06:34Z","timestamp":1719504394000},"page":"7619-7631","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Characterization of weakly nonlinear effects in relationship to transducer parameters in focused ultrasound therapy"],"prefix":"10.1002","volume":"51","author":[{"given":"Peng","family":"Xu","sequence":"first","affiliation":[{"name":"School of Biomedical Engineering Shanghai Jiao Tong University  Shanghai People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Wu","sequence":"additional","affiliation":[{"name":"Shanghai Shende Green Medical Era Healthcare Technology Co., Ltd  Shanghai People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guofeng","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Biomedical Engineering Shanghai Jiao Tong University  Shanghai People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,6,27]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejrad.2008.11.002"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/02656736.2020.1807617"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11547\u2010015\u20100580\u20107"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/cncr.25192"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.eururo.2018.06.006"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00330\u2010009\u20101520\u20105"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/ana.25126"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/219149"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.4103\/0973\u20101482.77064"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/58.139123"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/58.216837"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/58.216838"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.426941"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2018.2870064"},{"key":"e_1_2_8_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/02656736.2017.1422029"},{"key":"e_1_2_8_17_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.1531986"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2020.2967033"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0301\u20105629(02)00503\u20103"},{"key":"e_1_2_8_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ultras.2021.106591"},{"key":"e_1_2_8_21_1","doi-asserted-by":"publisher","DOI":"10.1088\/1674\u20101056\/18\/11\/052"},{"key":"e_1_2_8_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ultrasmedbio.2013.04.010"},{"key":"e_1_2_8_23_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.2161440"},{"key":"e_1_2_8_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ultras.2006.06.035"},{"key":"e_1_2_8_25_1","doi-asserted-by":"publisher","DOI":"10.3109\/02656736.2016.1160154"},{"key":"e_1_2_8_26_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/58\/8\/2537"},{"key":"e_1_2_8_27_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.3531553"},{"key":"e_1_2_8_28_1","doi-asserted-by":"publisher","DOI":"10.1134\/S1063771015030148"},{"key":"e_1_2_8_29_1","doi-asserted-by":"publisher","DOI":"10.1109\/TUFFC.2016.2619913"},{"key":"e_1_2_8_30_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.5126685"},{"key":"e_1_2_8_31_1","doi-asserted-by":"publisher","DOI":"10.1109\/TUFFC.2021.3074611"},{"key":"e_1_2_8_32_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.385942"},{"key":"e_1_2_8_33_1","doi-asserted-by":"publisher","DOI":"10.1109\/TUFFC.2009.1066"},{"key":"e_1_2_8_34_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/47\/11\/306"},{"key":"e_1_2_8_35_1","doi-asserted-by":"publisher","DOI":"10.1121\/1.4712021"},{"key":"e_1_2_8_36_1","doi-asserted-by":"publisher","DOI":"10.1109\/TUFFC.2019.2941795"},{"key":"e_1_2_8_37_1","doi-asserted-by":"crossref","unstructured":"WangK TeohE JarosJ TreebyBE Modelling nonlinear ultrasound propagation in absorbing media using the k\u2010Wave toolbox: experimental validation. 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