## 4 Discussion  
In this work, we have presented a method for real-time recombination correction in the dosimetry of dose rate varying radiotherapy treatments with arrays of ionization chambers. The method is based on the measurement of the instantaneous readout current (rather than only the total integrated charge) and the automatic correction according to such measurements. We have investigated the application of the method both with simulations of the response of ionization detectors (liquid- and air-filled chambers) and with preliminary experimental measurements taken with a liquid-filled ionization chamber, showing that the method seems feasible and accurate for the correction for recombination in dose-rate-varying radiotherapy verifications. Nonetheless, further experimental validation of this method is necessary to properly implement this methodology, in particular in different dose-per-pulse/dose-rate regimes and with different detection technologies. The method presented in this work can be used to correct the readout current in real time, without the need to save large amounts of data to perform the correction offline. This would require to perform the correction operation at a maximum frequency of \(\simeq\)kHz. Figure 5: Effect of recombination and recombination correction in the verification of a dynamic radiotherapy clinical treatment with a PTW729-like air-chamber. The dynamic dose rate corresponds to that of a lymph node tumor treatment, but scaled up to deliver a maximum dose per pulse of 1 (**A**), 2 (**B**) and 50 mGy (**C**). In the left panels we show for a particular pixel the raw readout current (red lines) and corrected readout current (blue lines) versus time. Notice that the dose per pulse in this pixel does not reach the maximum dose per pulse of the delivery. In the right panels we show a profile of the radiation field (the one shown in Figure 2), including generated charge (solid line), raw collected charge (dashed line), and corrected charge (dash-dot line). While in this work we did not perform the correction of the experimental data online, as the online recombination method was not implemented in the readout software at the time when the measurements were performed, we verified at a later stage that performing such operation online, at a frequency of 100-250 Hz is feasible with the software running on a standard personal computer. The analytic method that we developed for pulsed beams, based on Boag formula, seems adequate for correcting in the near saturation region (collection efficiencies \(\simeq\)0.9 or higher). This range includes most applications in conventional radiotherapy and FFF radiotherapy, both for liquid- and air-filled ionization chambers). For UDHR deliveries, where collection efficiencies can be well below the near-saturation region, Boag theory may not be reliable, and it may be necessary to use different parametrizations, as in Equation (3) or Equation (24). In addition, the pulse structure of UHDR deliveries may be quite different to the pulse structure used in conventional/FFF radiotherapy (which we have used in this work). In such situations, it is important to pay special attention to the selection of the integration time of the detector to avoid fluctuations and pulse overlapping. This issue has not been fully investigated in this work due to the lack of realistic delivery sequences for UHDR treatments. The methods that we propose in this work are similar to those described in [20], where the authors studied recombination in ionization chambers irradiated by dynamic Tomotherapy beams. They considered not only the temporal variation of the dose rate on the detector, but also the spatial variation of the dose rate (caused by dose gradients especially in the penumbra of the beams). However, in that paper, the authors relied on a Monte Carlo calculation of the dose rate on the detector, rather than on the measurement of the ionization current, which allows us to develop an online correction method like the one that we present in this paper.