## 1 Introduction  
In cancer therapy using radiation beams, ionizing particles such as photons are used to damage the DNA of cancer cells, terminate the cell reproduction and hence stop the tumour growth [1, 2]. As the external radiation beams have to pass through the patient's skin surface to reach the tumour, irradiation of normal tissues along the path of beam is inevitable. Therefore, the aim of radiotherapy is to give a high dose of radiation to the tumour, while at the same time sparing the surrounding normal tissues and organs. Recently, heavy-atom nanomaterials such as metallic and metal oxide nanoparticles (NPs) are studied as radiosensitizers in radiotherapy [3, 4, 5, 6]. The high atomic number of heavy-atom NPs increases the compositional atomic number of the tumour, when the particles are uptaken by the cancer cells. Energy deposition or radiation dose at the cancer cell therefore increases due to the enhancement of photoelectric effect, because of the high atomic number [7, 8]. This increase of photon absorption at the tumour relative to its surrounding also causes an imaging contrast enhancement, so that radiation staff can identify the tumour in an imaging modality, such as computed tomography, more accurately [9, 10, 11]. NPs not only act as a dose enhancer, but an effective imaging contrast agent in radiotherapy [12]. Although photoelectric effect is recognized as the main mechanism in the dose enhancement, it is found that the radiosensitization enhancement factors for the 35 keV (1.66) and 660 keV (1.18) photon beams are very close to measurements using gold (Au) NPs [13]. This is due to the increased low-energy electron yield and the range of the 660 keV photon beam. This finding opens the door of probability for nanoparticle-enhanced radiotherapy using MV photon beams [14]. For a medical linear accelerator (linac) to deliver a homogeneous dose distribution within the tumour volume, a flattening filter (FF) is required to be installed inside the linac head. The function of the filter is to flatten the photon beam profile produced by the target of the linac [15]. Although the application of FF can improve the dose distribution at the tumour, the filter has disadvantages of increasing the linac head scatter and decreasing of dose rate [16; 17]. Since the introduction of intensity modulated radiotherapy, multileaf collimator is employed to generate beam intensity modulation in treatment delivery [18]. As the dose distribution in the tumour can now be controlled by the multileaf collimator, FF can be removed from the linac head to produce a flattening-filter-free (FFF) photon beam. Without the beam attenuation from the FF, the output of the FFF photon beam can be increased from 600 to over 2,000 monitor units per minute [19; 20]. In addition, the FFF photon beam also avoids the head scatter from the FF, and shortens the treatment time. Nowadays, FFF photon beam has become a popular option to replace the FF beam in intensity modulated radiotherapy [21; 22; 23]. In nanoparticle-enhanced radiotherapy, treatment plan dosimetry between the FF and FFF photon beams is different [24]. It is because the FFF beam contains a greater number of low-energy photons due to the absence of the FF. These low-energy photons are removed by the FF, so beam hardening effect occurs in the FF photon beam [16; 17]. The difference in the photon energy spectrum between the FF and FFF beams leads to variations in dose and imaging contrast enhancement [10; 19]. This is because both the dose and imaging contrast enhancement depend mainly on the photoelectric effect, which is sensitive to the low-energy photon and the atomic number of the medium [7; 8]. It is therefore worthwhile to investigate the dose variation when the FF is removed from the linac in nanoparticle-enhanced radiotherapy. Monte Carlo simulation is used to determine the radiation dose and calculate the dose enhancement ratio in nanoparticle-enhanced radiotherapy [25; 26].