Measurement and simulation of Joule heating during treatment of B-16 melanoma tumors in mice with nanosecond pulsed electric fields.

Experimental evidence shows that nanosecond pulsed electric fields (nsPEF) trigger apoptosis in skin tumors. We have postulated that the energy delivered by nsPEF is insufficient to impart significant heating to the treated tissue. Here we use both direct measurements and theoretical modeling of the Joule heating in order to validate this assumption. For the temperature measurement, thermo-sensitive liquid crystals (TLC) were used to determine the surface temperature while a micro-thermocouple (made from 30 μm wires) was used for measuring the temperature inside the tissue. The calculation of the temperature distribution used an asymptotic approach with the repeated calculation of the electric field, Joule heating and heat transfer, and the subsequent readjustment of the electrical tissue conductivity. This yields a temperature distribution both in space and time. It can be shown that for the measured increase in temperature an unexpectedly high electrical conductivity of the tissue would be required, which was indeed found by using voltage and current monitoring during the experiment. Using impedance measurements within t(after)=50 μs after the pulse revealed a fast decline of the high conductivity state when the electric field ceases. The experimentally measured high conductance of a skin fold (mouse) between plate electrodes was about 5 times higher than those of the maximally expected conductance due to fully electroporated membrane structures (G(max)/G(electroporated))≈5. Fully electroporated membrane structure assumes that 100% of the membranes are conductive which is estimated from an impedance measurement at 10 MHz where membranes are capacitively shorted. Since the temperature rise in B-16 mouse melanoma tumors due to equally spaced (Δt=2 s) 300 ns-pulses with E=40 kV/cm usually does not exceed ΔΤ=3 K at all parts of the skin fold between the electrodes, a hyperthermic effect on the tissue can be excluded.