{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T15:04:27Z","timestamp":1785423867446,"version":"3.56.0"},"reference-count":80,"publisher":"National Academy of Sciences","issue":"29","license":[{"start":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T00:00:00Z","timestamp":1784160000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000781","name":"EC | European Research Council","doi-asserted-by":"publisher","award":["885155"],"award-info":[{"award-number":["885155"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100031060","name":"European High Performance Computing Joint Undertaking","doi-asserted-by":"publisher","award":["EHPC-REG-2025R02"],"award-info":[{"award-number":["EHPC-REG-2025R02"]}],"id":[{"id":"10.13039\/100031060","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,7,21]]},"abstract":"<jats:p>Ultrasound\u2013matter interactions underpin numerous biomedical and soft-matter applications, yet simulating these phenomena is challenging due to the large separation of viscous and sonic time scales. Continuum methods capture large-scale wave propagation but cannot resolve microscale interactions, while particle-based approaches offer molecular resolution but struggle with efficiency and stability at larger scales. We introduce a particle-based virtual ultrasound machine that uses a smoothed dissipative particle dynamics variant with an implicit pressure solver and a negative-pressure stabilization scheme, required to mimic acoustic propagation across medically relevant MHz\u2013GHz frequencies. We demonstrate its capabilities by modeling the acoustophoresis of encapsulated microbubbles, a key mechanism in ultrasound-mediated drug delivery. Beyond this application, the approach establishes a generalizable platform for simulating wave\u2013matter interactions in soft and biological materials, opening promising directions for computational studies of acoustics-driven phenomena in science and engineering.<\/jats:p>","DOI":"10.1073\/pnas.2610567123","type":"journal-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T16:59:54Z","timestamp":1784221194000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Virtual ultrasound machine operating in a GHz to MHz frequency range for particle-based biomedical simulations"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-9046-9868","authenticated-orcid":false,"given":"Urban","family":"\u010coko","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/050mac570","id-type":"ROR","asserted-by":"publisher"}],"name":"Theory Department, National Institute of Chemistry","place":["Ljubljana, Slovenia"]},{"id":[{"id":"https:\/\/ror.org\/05njb9z20","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana","place":["Ljubljana, Slovenia"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8466-8993","authenticated-orcid":false,"given":"Tilen","family":"Potisk","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/050mac570","id-type":"ROR","asserted-by":"publisher"}],"name":"Theory Department, National Institute of Chemistry","place":["Ljubljana, Slovenia"]},{"id":[{"id":"https:\/\/ror.org\/05njb9z20","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana","place":["Ljubljana, Slovenia"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0825-1659","authenticated-orcid":false,"given":"Matej","family":"Praprotnik","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/050mac570","id-type":"ROR","asserted-by":"publisher"}],"name":"Theory Department, National Institute of Chemistry","place":["Ljubljana, Slovenia"]},{"id":[{"id":"https:\/\/ror.org\/05njb9z20","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana","place":["Ljubljana, Slovenia"]},{"id":[{"id":"https:\/\/ror.org\/021018s57","id-type":"ROR","asserted-by":"publisher"}],"name":"Universitat de Barcelona Institute of Complex Systems","place":["Barcelona, Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,7,16]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2020.00124"},{"key":"e_1_3_4_2_2","doi-asserted-by":"crossref","unstructured":"T. M. Best K. E. Wilk C. T. Moorman D. O. Draper Low intensity ultrasound for promoting soft tissue healing: A systematic review of the literature and medical technology. Intern. Med. Rev. 2 271 (2016).","DOI":"10.18103\/imr.v2i11.271"},{"key":"e_1_3_4_3_2","first-page":"623","article-title":"Overview of therapeutic ultrasound applications and safety considerations","volume":"31","author":"Miller D.","year":"2012","unstructured":"D. Miller , Overview of therapeutic ultrasound applications and safety considerations. J. Ultrasound Med. Off. J. Am Inst. Ultrasound Med. 31, 623\u2013634 (2012).","journal-title":"J. Ultrasound Med. Off. J. Am Inst. Ultrasound Med."},{"key":"e_1_3_4_4_2","doi-asserted-by":"crossref","unstructured":"D. Neumann E. Kollorz \u201cUltrasound\u201d in Medical Imaging Systems: An Introductory Guide A. Maier S. Steidl V. Christlein J. Hornegger Eds. (Springer Cham (CH) 2018).","DOI":"10.1007\/978-3-319-96520-8_11"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-chembioeng-060817-084034"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-020-58133-0"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1093\/protein\/14.1.1"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0507603102"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.bpc.2011.07.004"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.3390\/pharmaceutics15061625"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2022.791145"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroscience.2021.03.011"},{"key":"e_1_3_4_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0929-8266(99)00013-0"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/TUFFC.2025.3566437"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1117\/1.3360308"},{"key":"e_1_3_4_16_2","first-page":"351","article-title":"Field: A program for simulating ultrasound systems","volume":"34","author":"Jensen J. A.","year":"1997","unstructured":"J. A. Jensen, Field: A program for simulating ultrasound systems. Med. Biol. Eng. Comput. 34, 351\u2013353 (1997).","journal-title":"Med. Biol. Eng. Comput."},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2022.106726"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2022.106774"},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2024.108169"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1103\/6l7z-bjzy"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492902000077"},{"key":"e_1_3_4_22_2","unstructured":"S. Y. Trofimov \u201cThermodynamic consistency in dissipative particle dynamics \u201d PhD thesis Technische Universiteit Eindhoven (2003)."},{"key":"e_1_3_4_23_2","doi-asserted-by":"publisher","DOI":"10.3389\/fmicb.2025.1558035"},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.1002\/SMMD.20230003"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1002\/smll.202003678"},{"key":"e_1_3_4_26_2","doi-asserted-by":"publisher","DOI":"10.1021\/acsanm.5c02783"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjst\/e2015-02415-x"},{"key":"e_1_3_4_28_2","first-page":"773","article-title":"On the forces acting on a small particle in an acoustical field in an ideal fluid","volume":"6","author":"Gor\u2019kov L. P.","year":"1962","unstructured":"L. P. Gor\u2019kov, On the forces acting on a small particle in an acoustical field in an ideal fluid. Sov. Phys. Doklady 6, 773 (1962).","journal-title":"Sov. Phys. Doklady"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1039\/C4LC01246A"},{"key":"e_1_3_4_30_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.analchem.5b01944"},{"key":"e_1_3_4_31_2","doi-asserted-by":"publisher","DOI":"10.1039\/C4LC00572D"},{"key":"e_1_3_4_32_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.analchem.7b01458"},{"key":"e_1_3_4_33_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.analchem.6b00323"},{"key":"e_1_3_4_34_2","doi-asserted-by":"publisher","DOI":"10.1039\/b910595f"},{"key":"e_1_3_4_35_2","first-page":"212","article-title":"On the acoustic radiation pressure on spheres","volume":"147","author":"King L. V.","year":"1934","unstructured":"L. V. King, On the acoustic radiation pressure on spheres. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 147, 212\u2013240 (1934).","journal-title":"Proc. R. Soc. Lond. Ser. A Math. Phys. Sci."},{"key":"e_1_3_4_36_2","first-page":"167","article-title":"Acoustic radiation pressure on a compressible sphere","volume":"5","author":"Yosioka K.","year":"1955","unstructured":"K. Yosioka, Y. Kawasima, Acoustic radiation pressure on a compressible sphere. Acta Acust. Acust. 5, 167\u2013173 (1955).","journal-title":"Acta Acust. Acust."},{"key":"e_1_3_4_37_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10404-013-1240-7"},{"key":"e_1_3_4_38_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.92.063309"},{"key":"e_1_3_4_39_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/38\/15\/003"},{"key":"e_1_3_4_40_2","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/42\/28\/285502"},{"key":"e_1_3_4_41_2","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2017.301"},{"key":"e_1_3_4_42_2","doi-asserted-by":"publisher","DOI":"10.1002\/cav.1499"},{"key":"e_1_3_4_43_2","doi-asserted-by":"publisher","DOI":"10.1039\/c2lc21068a"},{"key":"e_1_3_4_44_2","volume-title":"Fields of Force: A Course of Lectures in Mathematical Physics Delivered","author":"Bjerknes V.","year":"1906","unstructured":"V. Bjerknes, Fields of Force: A Course of Lectures in Mathematical Physics Delivered (Columbia University Press, 1906), vol. 1."},{"key":"e_1_3_4_45_2","doi-asserted-by":"publisher","DOI":"10.1063\/5.0238348"},{"key":"e_1_3_4_46_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2191050"},{"key":"e_1_3_4_47_2","doi-asserted-by":"publisher","DOI":"10.1142\/S012918310000002X"},{"key":"e_1_3_4_48_2","doi-asserted-by":"publisher","DOI":"10.1039\/D3SM00835E"},{"key":"e_1_3_4_49_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/s10051-021-00153-4"},{"key":"e_1_3_4_50_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-021-01098-3"},{"key":"e_1_3_4_51_2","doi-asserted-by":"publisher","DOI":"10.1021\/jp071097f"},{"key":"e_1_3_4_52_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1396848"},{"key":"e_1_3_4_53_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.aa.30.090192.002551"},{"key":"e_1_3_4_54_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4810754"},{"key":"e_1_3_4_55_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.1.18"},{"key":"e_1_3_4_56_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.67.026705"},{"key":"e_1_3_4_57_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2021.108171"},{"key":"e_1_3_4_58_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10483-018-2255-6"},{"key":"e_1_3_4_59_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2020.107261"},{"key":"e_1_3_4_60_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4802038"},{"key":"e_1_3_4_61_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11831-014-9124-x"},{"key":"e_1_3_4_62_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00773-004-0180-z"},{"key":"e_1_3_4_63_2","first-page":"731","article-title":"Analysis of impact wave pressure by particle method for compressible fluid","volume":"52","author":"Ikari H.","year":"2005","unstructured":"H. Ikari, H. Gotoh, T. Sakai, H. Tanioka, Analysis of impact wave pressure by particle method for compressible fluid. Annu. J. Coast. Eng. JSCE 52, 731\u2013735 (2005).","journal-title":"Annu. J. Coast. Eng. JSCE"},{"key":"e_1_3_4_64_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.coastaleng.2008.10.004"},{"key":"e_1_3_4_65_2","doi-asserted-by":"crossref","unstructured":"B. Solenthaler R. Pajarola Predictive-corrective incompressible SPH. ACM Trans. Graphics 28 Article No.: 40 (2009). https:\/\/doi.org\/10.1145\/1531326.1531346","DOI":"10.1145\/1531326.1531346"},{"key":"e_1_3_4_66_2","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392431"},{"key":"e_1_3_4_67_2","unstructured":"J. Bender SPlisHSPlasH_Library. GitHub. https:\/\/github.com\/InteractiveComputerGraphics\/SPlisHSPlasH. Accessed 12 August 2025."},{"key":"e_1_3_4_68_2","doi-asserted-by":"publisher","DOI":"10.1143\/ptp\/92.5.939"},{"key":"e_1_3_4_69_2","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0207(20000810)48:10<1445::AID-NME831>3.0.CO;2-9"},{"key":"e_1_3_4_70_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.12.030"},{"key":"e_1_3_4_71_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.06.016"},{"key":"e_1_3_4_72_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1995.1010"},{"key":"e_1_3_4_73_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6439"},{"key":"e_1_3_4_74_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1579475"},{"key":"e_1_3_4_75_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00397-010-0480-7"},{"key":"e_1_3_4_76_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ultsonch.2018.12.031"},{"key":"e_1_3_4_77_2","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1971"},{"key":"e_1_3_4_78_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2018.08.004"},{"key":"e_1_3_4_79_2","doi-asserted-by":"publisher","DOI":"10.1002\/fld.4074"},{"key":"e_1_3_4_80_2","unstructured":"U. \u010coko T. Potisk M. Praprotnik usSDPD. GitHub. https:\/\/github.com\/L17-Projects\/usSDPD. Deposited 3 July 2026."}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2610567123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T17:00:40Z","timestamp":1784221240000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2610567123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,16]]},"references-count":80,"journal-issue":{"issue":"29","published-print":{"date-parts":[[2026,7,21]]}},"alternative-id":["10.1073\/pnas.2610567123"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2610567123","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,16]]},"assertion":[{"value":"2026-03-24","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-06-18","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2610567123"}}