Numerical modelling and experimental verification of thermal effects in living cells exposed to high-power pulses of THz radiation

Abstract

Exposure of cells or biological tissues to high-power pulses of terahertz (THz) radiation leads to changes in a variety of intracellular processes. However, the role of heating effects due to strong absorption of THz radiation by water molecules still stays unclear. In this study, we performed numerical modelling in order to estimate the thermal impact on water of a single THz pulse as well as a series of THz pulses. A finite-element (FE) model that provides numerical solutions for the heat conduction equation is employed to compute the temperature increase. A simple expression for temperature estimation in the center of the spot of THz radiation is presented for given frequency and fluence of the THz pulse. It has been demonstrated that thermal effect is determined by either the average power of radiation or by the fluence of a single THz pulse depending on pulse repetition rate. Human dermal fibroblasts have been exposed to THz pulses (with an energy of [Formula: see text] and repetition rate of 100 Hz) to estimate the thermal effect. Analysis of heat shock proteins expression has demonstrated no statistically significant difference ([Formula: see text]) between control and experimental groups after 3 h of irradiation.

Figure 1

Experimental setup for cell irradiation. (a) Schematic diagram. (b) Cross-section of the water cylinder used in numerical modelling of heat transfer caused by exposure to THz radiation: b and d are the radius and the thickness of the cylinder, respectively, a is the radius of the THz beam.

Figure 2

Temperature distributions of water for a single THz pulse. (a) Radial (at $z=0$) and (b) axial (at $r=0$) temperature dependencies at various time instants. Spatial temperature distribution (c) at the end of the THz pulse ($E_{\mathrm{THz}}^{\ast }=15[\mathrm{\mu }\text{J}]$, $t_{\mathrm{h}}=515[\text{fs}]$) and (d) when the next THz pulse comes ($t_{\mathrm{c}}=10[\text{ms}]$ for $f_{\mathrm{p}}=100[\text{Hz}]$).

Figure 3

Absorption results for a series of THz pulses. (a) Comparison between the radial (at $z=0$) and axial (at $r=0$) temperature distributions for the pulse model (dotted lines) and those obtained for the CW model (dashed lines). (b) Temporal evolution of temperature T(0, 0) in the beam’s center.

Figure 4

Extending the limits of the FE-model application. (a) Temperature increase $\mathrm{\Delta }T(0,0)$ in the beam’s center and absorption coefficient ${\alpha }^{\prime }$ as a function of radiation frequency $\nu$; $\mathrm{\Delta }T(0,0)$ as a function of pulse energy and peak power (inset). (b) Temperature increase $\mathrm{\Delta }{T}_{\nu }$ in the beam’s center as a function of frequency for various initial temperatures $T_0$. See Data File for underlying values.

Figure 5

HSPs expression in human fibroblasts. (a) Experimental group after exposure to intense pulses of THz radiation for 180 min. (b) Control group (no irradiation or external heating). (c) Cells after incubation at 40${}^{\circ }$C in positive control group, (d) Mean fluorescence intensity of secondary goat anti-mouse IgG (H + L) antibodies. $N>50$ cells/group. Asterisks indicate a statistically significant difference (**$p<0.05$ by Mann-Whitney t-test).