OBJECTIVE: During any radiological procedure, it is important to know the dose to be-administered to the patient and this can be done by estimating the output of the X-ray tube either with a dosimeter or with a mathematical equation or Monte Carlo simulations. The aim of this work is to develop a new mathematical model equation (NMME) for estimating the output of high-frequency X-ray tubes.
METHODS: To achieve this, data collected from ten machines in many regions of Cameroon were used (for nine machines) to build an initial model that does not take into account the anode angle and the tenth machine was used to test the model. Using the SpekCalc software, some simulations were carried out to evaluate the influence of the anode angle. This allowed the NMME to be proposed.
RESULTS: The deviations frequencies between 0.65% and 19.61% were obtained by comparing the output values obtained using initial model with the measured values. The statistical hypothesis test showed that the estimated values using initial model and NMME are in agreement with those measured unlike the Kothan and Tungjai model. For the tenth machine, the percentage difference between estimated and measured values is less than 8 %.
CONCLUSIONS: These results show that the proposed model performed better than the previous models. In the absence of a dosimeter, the NMME could be used to estimate the output of high frequency X-ray machines and therefore the radiation doses received by patients during diagnostic X-ray examinations.

According to the National Institute of Public Health, prostate cancer (PCa) is the leading cause of cancer death in Mexican men, highly associated with aggressiveness, resistance to treatment, and metastatic spread (Bharti et al., 2019) mediated by activation of the hypoxia-inducible factor 1 (HIF-1α). The objective of the present study was to evaluate the participation of HIF-1α activation in the radiobiological response of the human prostate adenocarcinoma cell line LNCaP, describing the phenomena with a mathematical model. Four groups were formed under different exposure conditions, including hypoxic cells treated with CoCl2 (300 μM for 22 h) with or without hypoxia-inducible factor inhibitor (150 nM chetomin for 4 h added after an incubation period of 18 h with CoCl2, just before completing the incubation period of 22 h). They were exposed to a source of 60Co in a dose range between 2 and 10 Gy to obtain survival curves that are fitted to a mathematical model. CoCl2 or chetomin treatments do not affect the viability of LNCaP cells that remained unchanged after irradiation. CoCl2 induced hypoxia reduces the survivability of LNCaP, and obstruction of HIF-1α signaling with chetomine produces a slight radioprotective effect. As others report, the genetic reprogramming induced by HIF-1α activation acts as an intrinsic agent that selects cells with more aggressive behavior (Pressley et al., 2017), while chetomin protects cells from death due to its scavenger properties. Interestingly, treatment with chetomin of cells induced to hypoxia (HIF-1 activation with CoCl2) produces a significant reduction in the radioresistance of LNCaP cells, demonstrating that the simultaneous use of chetomin and gamma radiation is an effective option for the treatment of hypoxic prostate cancer. At the molecular level, we suggest that the selective force exerted by HIF-1α depends on the production of free radicals by radiation. The proposed mathematical model showed that the rate of change in cell survival as a function of radiation dose is proportional to the product of two functions, one that describes cell death and the other that describes natural or artificial resistance to radiation.