Electron-hole liquid in biological tissues under ultra high dose rate ionizing radiation

TL;DR

The paper addresses how ultra-high dose-rate radiation affects biological tissues by proposing electron-hole liquid formation as a mechanism for tissue sparing. It develops a quantitative framework linking ionization, EHL binding, and recombination kinetics, deriving a dose threshold $D_{min}$ and a dose-rate threshold $\dot{D}_{min}$. The model predicts that an EHL state can persist after irradiation, suppressing secondary radical generation and yielding a dose-rate dependent sparing effect, with dynamics influenced by dielectric dispersion. Limitations include neglecting biological processes, sensitivity to parameter choices, and the need for experimental validation; the work provides a physically grounded explanation for FLASH RT phenomena and guides future tests of EHL signatures.

Abstract

We develop a quantitative model of ionization processes in biological tissues under Ultra High Dose Rate (UHDR) radiation. The underlying conjecture is that of electron-hole liquid (EHL) forming in water based substances of biological tissues. Unlike the earlier known EHL in semiconductor crystals, the charge carriers here are low mobile due to strong interactions with the background (solvated electrons, etc.); hence, EHL resembling ionic melts. Similar to all ionic systems, the Coulomb coupling makes that EHL energetically favorable that leads to recombination barriers suppressing subsequent structural transformations. In particular, generation of secondary reactive species in such EHL becomes limited translating into reduction of biological damages and tissue sparing effect. We show how these processes are sensitive to the tissue quality and frequency dispersion of the dielectric permittivity. Equations for dose and dose rate defining the sparing thresholds are derived.

Figures (5)

• Figure 1: Radiation induced ionization depending on dose rate and energy. Dark (white) circles represent electrons (holes). From right to left: (1) plasma of weakly interacting electrons and holes generated with low dose rates high energy radiation; (b) excitons, i. e. coupled electron - hole pairs generated with higher dose rates and close to the absorption edge radiation; (3) biexcitons which are coupled pairs of excitons forming with increase of exciton concentration; (4) a droplet of electron hole liquid under high dose rate of well absorbed radiation.
• Figure 2: Typical temporal dependencies of EHL ($n(t)$) and RSS ($R(t)$) rates assuming strong enough binding ($L>2$).
• Figure 3: A typical temporal dependence of EHL concentration with initial strong binding ($L>2$) upon switching off the radiation source.
• Figure 4: A calculated sketch of sparing effect showing how irradiation created modifications decrease with the dose rate.
• Figure 5: A temporal dependence of EHL concentration $n$ for recombination and dielectric permittivity relaxation processes acting simultaneously. The corresponding times are shown in the figure will serve as our example. The maximum point reflects increase in EHL concentration before the dielectric relaxation effects starts. Dashed line represents an approximation of the purely exponential decay $\exp(-t/\tau _{\kappa})$.