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Conjecture of classical e-h liquid for understanding the FLASH modality of radiation cancer treatment

Diana Shvydka1,*, Victor Karpov2,†, and Nilendu Gupta1,‡

  • *Contact author: diana.shvydka@osumc.edu
  • †Contact author: victor.karpov@utoledo.edu
  • ‡Contact author: Nilendu.Gupta@osumc.edu
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APS Open Sci. 1, 000114 – Published 28 August, 2026

DOI: https://doi.org/10.1103/72k1-gmwt

Abstract

We consider physics behind the FLASH modality of cancer radiation treatment, where extremely short treatment times are achieved with ultrahigh dose rates maintaining the conventional antitumor effectiveness and yet substantially reducing damage to normal tissues (sparing effect). The difference in responses between normal and tumor tissues is attributed here to the structure transformation rates related to their morphologies: ordered in the normal tissues versus disordered in tumor tissues. Correspondingly different are nonequilibrium charge densities accumulated in the two phases under ionizing radiation. In normal tissues, it is high enough to form a classical electron-hole liquid (EHL). The low EHL diffusivities slow down the generation of biologically active free radicals, hence sparing effect. To the contrary, a disordered tumor tissue renders efficient energy relaxation channels forming free radicals. We describe the FLASH thresholds for doses and dose rates.

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References (71)

  1. D. L. Dewey and J. W. Boag, Modification of the oxygen effect when bacteria are given large pulses of radiation, Nature (London) 183, 1450 (1959).
  2. J. Farr, V. Grilj, V. Malka, S. Sudharsan, and M. Schippers, Ultra-high dose rate radiation production and delivery systems intended for FLASH, Med. Phys. 49, 4875 (2022).
  3. R. Schulte, C. Johnstone, S. Boucher, E. Esarey, C. G. R. Geddes, M. Kravchenko, S. Kutsaev, B. W. Loo, Jr, F. Meot, B. Mustapha, K. Nakamura, E. A. Nanni, L. Obst-Huebl, S. E. Sampayan, C. B. Schroeder, K. Sheng, A. M. Snijders, E. Snively, S. G. Tantawi, and J. Van Tilborg, Transformative technology for FLASH radiation therapy, Appl. Sci. 13, 5021 (2023).
  4. C. L. Limoli and M.-C. Vozenin, Reinventing radiobiology in the light of FLASH radiotherapy, Annu. Rev. Cancer Biol. 7, 1 (2023).
  5. J. C. L. Chow and H. E. Ruda, Mechanisms of action in FLASH radiotherapy: A comprehensive review of physicochemical and biological processes on cancerous and normal cells, Cells 13, 835 (2024).
  6. M.-C. Vozenin, B. W. Loo, Jr., S. Tantawi, P. G. Maxim, D. R. Spitz, C. Bailat, and C. L. Limoli, FLASH: New intersection of physics, chemistry, biology, and cancer medicine, Rev. Mod. Phys. 96, 035002 (2024).
  7. G. Rosini, E. Ciarrocchi, and B. D’Orsi, Mechanisms of the FLASH effect: Current insights and advances, Front. Cell Dev. Biol. 13, 1575678 (2025).
  8. T. Feng, T. He, W. Ye, and L. Xiang, Influence factor and mechanism of FLASH effect, Front. Oncol. 15, 1669228 (2025).
  9. M.-C. Vozenin, P. Montay-Gruel, P. Tsoutsou, and C. L. Limoli, Mechanisms, challenges and opportunities for FLASH radiotherapy in cancer, Nat. Rev. Cancer 26, 62 (2026).
  10. D. Shvydka and V. Karpov, Electron-hole liquid in biological tissues under ultrahigh-dose-rate ionizing radiation, arXiv:2510.10786v1.
  11. D. Shvydka and V. Karpov, Electron-hole liquid in biological tissues under ultra high dose rate ionizing radiation, Phys. Rev. Appl. 25, 064023 (2026).
  12. D. M. McDonald and P. L. Choyke, Imaging of angiogenesis: From microscope to clinic, Nat. Med. 9, 713 (2003).
  13. P. Kenny (illustrator), Normal and cancer cells structure, National Cancer Institute, AV-9004-3728, https://visualsonline.cancer.gov/details.cfm?imageid=2512. This image is in the public domain and can be freely reused.
  14. The standard sketch of crystalline and amorphous silicon structures. The current image is copied from photovoltaic knowledge, https://www.memodo.at/m/photovoltaik-wissen/pv-wiki/amorphes-silizium/.
  15. N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials, 2nd ed., Oxford Classic Texts in the Physical Sciences (Oxford University Press, Oxford, 2012).
  16. See Supplemental Material at http://link.aps.org/supplemental/10.1103/72k1-gmwt for the explanation of the physics of radiativeless recombination in disordered system.
  17. W. A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond, Dover Books on Physics (Dover Publications, Mineola, NY, 1989).
  18. T. Bischoff, I. Reshetnyak, and A. Pasquarello, Band gaps of liquid water and hexagonal ice through advanced electronic-structure calculations, Phys. Rev. Res. 3, 023182 (2021).
  19. A. Shimkevich, Electrochemical view of the band gap of liquid water for any solution, World J. Condens. Matter Phys. 04, 243 (2014).
  20. B. I. Shklovskii, Model for surface recombination, Pisma ZhETF 44, 95 (1986) [Sov. Phys. JETP Lett. 14, 123 (1986)].
  21. S. D. Baranovskii, V. G. Karpov, and B. I. Shklovskii, Nonradiative recombination in noncrystalline semiconductors, Zh Eksp. Teor. Fiz. 94, 278 (1988) [Sov. Phys. JETP 67, 588 (1988)].
  22. P. A. Riley, Free radicals in biology: Oxidative stress and the effects of ionizing radiation, Int. J. Radiat. Biol. 65, 27 (1994).
  23. J.-P. Jay-Gerin, Fundamentals of water radiolysis, Encyclopedia 5, 38 (2025).
  24. L. V. Keldysh, Electron-hole drops in semiconductors, Sov. Phys. Usp. 13, 292 (1970).
  25. Ya Pokrovskii, Condensation of non-equilibrium charge carriers in semiconductors, Phys. Status Solidi A 11, 385 (1972).
  26. S. G Tikhodeev, The electron-hole liquid in a semiconductor, Sov. Phys. Usp. 28, 1 (1985).
  27. L. V. Keldysh, Electron-hole liquid in semiconductors, Contemp. Phys. 27, 395 (1986).
  28. K. Ogawa, T. Ohyama, and E. Otsuka, Effect of deep impurity on recombination lifetime of a large electron-hole drop in strained germanium, Solid State Commun. 57, 231 (1986).
  29. R. Shimano, M. Nagai, K. Horiuch, and M. Kuwata-Gonokami, Formation of a high Tc electron-hole liquid in diamond, Phys. Rev. Lett. 88, 057404 (2002).
  30. M. Nagai, R. Shimano, K. Horiuchi, and M. Kuwata-Gonokami, Creation of supercooled exciton gas and transformation to electron-hole droplets in diamond, Phys. Rev. B 68, 081202 (2003).
  31. R. Sauer, N. Teofilov, and K. Thonke, Exciton condensation in diamond, Diamond Relat. Mater. 13, 691 (2004).
  32. A. E. Almand-Hunter, H. Li, S. T. Cundiff, M. Mootz, M. Kira, and S. W. Koch, Quantum droplets of electrons and holes, Nature (London) 506, 471 (2014).
  33. A. K. Poonia, P. Yadav, B. Mondal, D. Mandal, P. Taank, M. Shrivastava, A. Nag, A. Agarwal, and K. V. Adarsh, Room-temperature electron-hole condensation in direct-band-gap semiconductor nanocrystals, Phys. Rev. Appl. 20, L021002 (2023).
  34. D. Emin, Polarons (Cambridge University Press, Cambridge, New York, 2013).
  35. R. Ghosh and F. C. Spano, Excitons and polarons in organic materials, Acc. Chem. Res. 53, 2201 (2020).
  36. J. H. Bombile, M. J. Janik, and S. T. Milner, Polaron formation mechanisms in conjugated polymers, Phys. Chem. Chem. Phys. 20, 317 (2018).
  37. E. M. Conwell and S. V. Rakhmanova, Polarons in DNA, Proc. Natl. Acad. Sci. USA 97, 4556 (2000).
  38. C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, Hoboken, NJ, 1996).
  39. Wikipedia article “Madelung constant,” https://en.wikipedia.org/w/index.php?title=Madelung_constant&oldid=1282359272.
  40. N. Takenaka, S. Ko, A. Kitada, and A. Yamada, Liquid Madelung energy accounts for the huge potential shift in electrochemical systems, Nat. Commun. 15, 1319 (2024).
  41. J. Ma, U. Schmidhammer, and M. Mostafavi, Direct evidence for transient pair formation between a solvated electron and H3O+ observed by picosecond pulse radiolysis, J. Phys. Chem. Lett. 5, 2219 (2014).
  42. M. Tannino, F. Mangini, L. Dinia, and F. Frezza, A heuristic model to evaluate the dielectric properties of human tissues at microwave band based on water and solid content, J. Eng. Appl. Sci. 70, 43 (2023).
  43. M. Checa, R. Millan-Solsona, N. Blanco, E. Torrents, R. Fabregas, and G. Gomila, Mapping the dielectric constant of a single bacterial cell at the nanoscale with scanning dielectric force volume microscopy, Nanoscale 11, 20809 (2019).
  44. V. N. Abakumov, V. I. Perel and I. N. Yassievich, Nonradiative recombination in semiconductors, in Modern Problems in Condensed Matter Sciences, edited by V. M. Agranovich and A. A. Maradudin (North-Holland, Amsterdam, 1991), pp. 1–320.
  45. F. Le Formal, S. R. Pandlebury, M. Cornuz, S. Tilley, M. Gratzel, and J. R. Durant, Back electron hole recombination in hematite photoanodes for water splitting, J. Am. Chem. Soc. 136, 2564 (2014).
  46. J. Zimmermann and U. van Rienen, Ambiguity in the interpretation of the low-frequency dielectric properties of biological tissues, Bioelectrochemistry 140, 107773 (2021).
  47. C. Matzler and U. Wegmuller, Dielectric properties of fresh water ice at microwave frequencies, J. Phys. D: Appl. Phys. 20, 1623 (1987).
  48. D. S. Shen, J. P. Conde, V. Chu, and S. Wagner, Carrier lifetime in amorphous semiconductors, J. Appl. Phys. 75, 7349 (1994).
  49. S. Gupta, J. L. Inman, J. De Chant, L. Obst-Huebl, K. Nakamura, S. M. Costello, S. Marqusee, J.-H. Mao, L. Kunz, R. Paisley, M.-C. Vozenin, A. M. Snijders, and C. Y. Ralstona, A novel platform for evaluating dose rate effects on oxidative damage to peptides: Toward a high-throughput method to characterize the mechanisms underlying the FLASH effect, Radiat. Res. 200, 523 (2023).
  50. F. Del Debbio, M. S. Bertilacchi, A. Cavalieri, G. Gadducci, N. Giannini, A. Gonnelli, F. C. Zanacchi, B. Noferi, A. Catanzariti, M. De Felice, C. Giacomelli, F. Di Martino, C. Martini, E. Da Pozzo, F. Paiar, and S. Capaccioli, Mitigating the side effects of conventional radiotherapy: Deep examination of the FLASH effect on human healthy bronchial epithelial cell line, Cancer Treat. Res. Commun. 44, 100961 (2025).
  51. J. P. Keene, Kinetics of radiation-induced chemical reactions, Nature (London) 188, 843 (1960).
  52. Dietrich Schulte-Frohlinde and Klaus Eiben, Solvatisierte elektronen in eingefrorenen Lösungen, Z. Naturforsch. A 17, 445 (1962).
  53. E. J. Hart and J. W. Boag, Absorption spectrum of the hydrated electron in water and in aqueous solutions, J. Am. Chem. Soc. 84, 4090 (1962).
  54. J. P. Keene, Optical absorptions in irradiated water, Nature (London) 197, 47 (1963).
  55. T. Kusumoto, A. Danvin, T. Mamiya, A. Arnone, S. Chefson, C. Galindo, P. Peaupardin, Q. Raffy, N. Kamiguchi, D. Amano, K. Sasai, T. Konishi, and S. Kodaira, Dose rate effects on hydrated electrons, hydrogen peroxide, and a OH radical molecular probe under clinical energy protons, Radiat. Res. 201, 287 (2024).
  56. T. Zhang, C. Stengl, L. Derksen, K. Palskis, K. Koritsidis, K. Zink, S. Adeberg, G. Major, D. Weishaar, U. Theiß, J. Jin, M. F. Spadea, E. Theodoridou, J. Hesser, K.-S. Baumann, and J. Seco, Analysis of hydrogen peroxide production in pure water: Ultrahigh versus conventional dose-rate irradiation and mechanistic insights, Med. Phys. 51, 7439 (2024).
  57. X. Cao, A. Parks, W. Thomas, M. S Reed, W. S Culberson, and B. W Pogue, Hydrated electron yield dependence on instantaneous dose rates with electron ultra-high dose rate (UHDR) irradiation, Phys. Med. Biol. 70, 125013 (2025).
  58. A. M. Smith, A. A. Lee, and S. Perkin, The electrostatic screening length in concentrated electrolytes increases with concentration, J. Phys. Chem. Lett. 7, 2157 (2016).
  59. D. Shvydka and V. Karpov, Underscreening and related phenomena in concentrated electrolytes, arXiv:2606.15492.
  60. A. Alanazi, J. Meesungnoen, and J.-P. Jay-Gerin, A computer modeling study of water radiolysis at high dose rates. Relevance to FLASH radiotherapy, Radiat. Res. 195, 146 (2021).
  61. H. Kacem, A. Almeida, N. Cherbuin, and M.-C. Vozenin, Understanding the FLASH effect to unravel the potential of ultra-high dose rate irradiation, Int. J. Radiat. Biol. 98, 506 (2022).
  62. G. Blain, J. Vandenborre, D. Villoing, V. Fiegel, G. R. Fois, F. Haddad, C. Koumeir, L. Maigne, V. Métivier, F. Poirier, V. Potiron, S. Supiot, N. Servagent, G. Delpon, and S. Chiavassa, Proton irradiations at ultra-high dose rate vs. conventional dose rate: Strong impact on hydrogen peroxide yield, Radiat. Res. 198, 318 (2022).
  63. P. Froidevaux, V. Grilj, C. Bailat, W. R. Geyer, F. Bochud, and M.-C. Vozenin, FLASH irradiation does not induce lipid peroxidation in lipids micelles and liposomes, Radiat. Phys. Chem. 205, 110733 (2023).
  64. T. Konishi, K. T. Kusumoto, Y. Hiroyama, A. Kobayashi, T. Mamiya, and S. Kodaira. Induction of DNA strand breaks and oxidative base damages in plasmid DNA by ultra-high dose rate proton irradiation, Int. J. Radiat. Biol. 99, 1405 (2023).
  65. P. Wardman, Radiation-chemical perspective of the radiobiology of pulsed (high dose-rate) radiation (FLASH): A postscript, Radiat. Res. 201, 87 (2024).
  66. H. Kacem, L. Kunz, P. Korysko, J. Ollivier, P. Soutsou, A. Martinotti, V. Rieker, J. Bateman, W. Farabolini, G. Baldacchino, B. W. Loo Jr., C. L. Limoli, M. Dosanjh, R. Corsini, and M.-C. Vozenin, Modification of the microstructure of the CERN-CLEAR-VHEE beam at the picosecond scale modifies ZFE morphogenesis but has no impact on hydrogen peroxide production, Radiother. Oncol. 209, 110942 (2025).
  67. L. V. Kunz, R. Schaeferd, H. Kacema, J. Ollivier, M. Togno, F. Chappuis, D. Weber, A. Lomax, C. L. Limoli, S. Psoroulas, and M.-C. Vozenin, Plasmid DNA strand breaks are dose rate independent at clinically relevant proton doses and under biological conditions, Radiat. Res. 203, 214 (2025).
  68. I. Rabeya, J. Meesungnoen, and J.-P. Jay-Gerin, Oxygen depletion and the role of cellular antioxidants in FLASH radiotherapy: Mechanistic insights from Monte Carlo radiation-chemical modeling, Antioxidants 14, 406 (2025).
  69. L. Alhaddad, A. N. Osipov, and S. Leonov, FLASH radiotherapy: Benefits, mechanisms, and obstacles to its clinical application, Int. J. Mol. Sci. 25, 12506 (2024).
  70. L. Portier, P. Daira, B. Fourmaux, S. Heinrich, M. Becerra, C. Fouillade, N. Berthault, M. Dutreix, A. Londono-Vallejo, P. Verrelle, N. Bernoud-Hubac, and V. Favaudon, Differential remodeling of the oxylipin pool after FLASH versus conventional dose-rate irradiation in vitro and in vivo, Int. J. Radiat. Oncol. Biol. Phys. 119, 1481 (2024).
  71. G. Adrian, J.-L. Ruan, S. Paillas, C. R. Cooper, and K. Petersson, In vitro assays for investigating the FLASH effect, Expert Rev. Mol. Med. 24, e10 (2022).

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APS Open Sci. 1, 000114– Published 28 August, 2026
Vol. 1
  • Received 27 April 2026
  • Revised 15 July 2026
  • Accepted 18 August 2026
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