Figure 1 shows the X-ray machines that failed the HVL test at 80 kV with their corresponding dose output. Out of the 26 machines, 14 had a mobile orientation while 12 were fixed. About 54% of the 26 machines produced dose output within an optimal range of 0.025 mGy/mAs - 0.080 mGy/mAs. An implication of the failure of the HVL test is that the HVL of the machine at any selected kV was below the recommended regulatory limit, indicating inadequate filtration of the damaging soft X-rays. Since the patient receives an optimal dose even at HVLs below the recommended limit, the appropriate action to be recommended for such machines is complicated. With a little modification to Edmond’s equation [8] (Poletti, 1994), an inverse relationship exists between HVL and dose as shown in Equation (2). Noting that the kV accuracy test has passed, the facility may consider adding additional filters of either aluminum or copper material to normalize the HVL. However, this may lower the patient’s dose and contrast, which affects the planned purpose of the imaging. For most machines, the variation of X-ray tube potential results in the variation of the filtration automatically [8] (Poletti, 1994).

$\text{Dose}=\frac{{\text{kV}}^n\ast \text{mAs}}{\text{FFD}}\left(\frac{1}{\text{HVL}}+0.114\right)$ (2)

A total of 7 X-ray machines (~31%) of the 26 machines produced doses below the lower limit of 0.025 mGy/mAs. This is rather more complicated because we would expect a high dose because of the less filtration of the X-ray beam. In this case, the patients are likely to receive very low doses, and hence, the purpose of the diagnosis may not be achieved. This may result in cases of repeated exposures, and or misdiagnosis, and hence patients may receive unjustified doses. As already discussed, the HVL reduces beam intensity and increases the average beam energy, which is controlled by the tube potential/kVp variation [1] (Sprawls, 2001). This does not affect the number of photons in the spectrum that contribute to the dose, which is controlled by the mA/tube current modulation as shown in Equation (2). Therefore, while HVL may affect the dose output, the dose does not affect HVL.

Three X-ray machines (GG, RR & ZZ) produced doses greater than the upper limit of the optimal dose range, which subjects the patients to higher doses. Therefore, we recommend immediate action on such machines not to be used for medical exposures till the appropriate action is taken to correct the dose. The X-ray machine RR had the lowest HVL at each kV compared to other machines, though all the machines had HVLs less than the regulatory limit at each kV. The HVL dose relationship for the 3 machines does not comply with Equation (2), otherwise, RR should have the greatest dose. This is because other factors contribute to the dose specific to generator type, manufacturer, and age. Machines that have different manufacturers of the collimator, X-ray tube, and generator tend to fail the kV output, and hence HVL, due to mismatched tube-generator characteristics [4] [17] [18] (AAPM, 2002; European Commission: Directorate-General for Research and Innovation, 1996; IAEA, 2023). Additionally, the old X-ray machines require frequent calibration services to maintain compliance with the regulatory standards of dose and HVL. Past studies have shown that 1- and 2-pulse waveforms yield softer X-ray spectra associated with increased doses to the patient [10] (International Atomic Energy Agency (IAEA), 2014). Some of these isolated cases of inconsistencies in machine performance that affect the HVL dose relationship have been identified during our routine inspections, though they lack the detailed documentation for further assessment. This study, therefore, identifies the knowledge and literature gap to be addressed in subsequent research works.

For all the above three cases, the immediate recommendation is to add additional filter plates of aluminum or copper to increase the HVL thickness. However, this should be done after an adequate investigation that checks the accuracy of the tube current and timer for machines with different mA and timer consoles. We note from Equation (2) that the tube current has a direct impact on dose output. Other than the accuracy of the tube output, other tests, for example, reproducibility and power quality, also define the quality of kVp [19] [20] (Godfrey et al., 2015; Hjouj et al., 2022). In this study, all 26 machines had good kV reproducibility, shown by a coefficient of variation of less than 10% at each kV setting. However, we could not assess the power quality of each machine, which was a limitation of the study. Therefore, as we conclude in this case, the type of orientation of the X-ray machine may not necessarily affect the performance standard of HVL. However, from the general observation during routine inspections, the failure rate of the HVL test was higher in mobile than in fixed X-ray machines. This might be due to;

a) Old-aged mobile X-ray machines manufactured before 2012 with low HVL compared to the regulatory standards [4] [9] [20] (Faulkner et al., 2012; Hjouj et al., 2022; IAEA, 2023).

b) Mobile X-ray machines are meant to be used for emergencies, but not for general radiography, which results in overloading and hence faster deterioration of their performance [21] [22] (Kartika & Savitri, 2020; Nevada Division of Public and Behavioral Health (DPBH), 2023).

Most of these types of machines were imported into the country even before the establishment of regulatory standards. We also note that the current trend of machines being imported into the country generally has high HVL standards for adequate filtration.

From Table 2 , it’s noted that all machines that had HVL above 2.9 mmAl at 80 kV passed the HVL test. The number of X-ray machines in each class was 5, 19, 10, and 4 for moderate, high, very high, and extreme high, respectively. Figure 2 shows the X-ray machines for the different classifications above the regulatory limit and their variation of measured dose output.

Generally, all the machines exhibited a phenomenon in Equation (2), except X-ray machines AB in the moderate class and QQ in the high class. It’s observable that as the HVL values increased from moderate to extremely high, the dose continuously lowered below the lower limit of the optimal dose range of 0.025 mGy/mAs. The high HVL values imply that there is excessive filtration of the X-ray spectrum, which may lower the dose to the patient. This is important for dose minimization to the patient; however, this may affect the optimal dose required to achieve the purpose of imaging for proper diagnosis. It’s noted during the inspections that some machines with HVL values above the recommended limit, similar to this case, produced doses within the recommended optimal range. The excessive filtration greatly reduces the low-energy photons, which significantly reduces the contrast. At low photon energies, the absorption properties of body tissues vary [23] [24] (Kadri & Alfuraih, 2019; Sandell & Zhu, 2011). Therefore, the reduction in contrast may only be perceived at very high values of HVLs greater than the recommended regulatory values [8] (Poletti, 1994).

For these cases, we recommend checking for removable additional filters to minimize the filtration. However, this should be done after an adequate investigation, including checking the geometry setup and the accuracy of the tube’s current output [4] (IAEA, 2023). For the modern trend of X-ray machines, the inverse relationship between dose and HVL may not directly apply. We can observe this from the recent modifications in the traditional Edmond’s equation, refer to [25] [26] (Kothan & Tungjai, 2011; Simo et al., 2021) for details. This is because of the improved technologies of image processing that ensure a better quality image even at minimal doses like digital radiography systems [27] - [29] (Lee et al., 2020; Ou et al., 2021; Singh, 2023).

In a follow-up exercise on the previous inspection findings for the machines AB and QQ, we established the following: 1) the fixed X-ray machine AB, manufactured in 2013, had no past inspection history, and 2) the mobile X-ray machine QQ, manufactured in 1991, had been inspected about four times. Table 3 shows a summary of its performance results at set parameters of 80 kV, 20 mAs, and FFD of 100 cm.

We noticed the variation of the results of performance parameters during different inspection visits, despite no actions of machine repair or calibration were recorded. We established that the facility had resorted to operating the machine using a generator since there was an unstable power supply. Previous studies [30] [31] (Ngounou et al., 2015; Zhang et al., 2011) have noted that the low stability of the power supply can affect the performance of the X-ray machine. Therefore, it’s recommended to maintain a high power supply for any operating X-ray equipment to ensure the production of stable and constant X-rays with enough penetrating power. The cases of power instability have been reported to affect mostly mobile X-ray machines, which use battery charging systems for power supply. Therefore, we always recommend assessing performance parameters for such machines when the batteries are fully charged.

The graphical representation in Figure 3 above shows the inverse relationship between HVL and dose, though the equation of the linear relationship of the above graphs may not estimate the accurate dose. A detailed statistical analysis using Excel is shown in Table 4 .

The correlation coefficient (multiple R) tends to zero rather than 1 for both A and B machines, implying a weak correlation between HVL and dose for the two cases. However, the dose HVL relationship is explained better by group B machines that passed the HVL test, shown by the higher F-statistic value compared to group A machines. A negative HVL coefficient for both cases confirms the discussion in the above section that an increase in HVL decreases the dose, which is in line with the previous studies [8] [24] [28] [32] (Ofori et al., 2016; Ou et al., 2021; Poletti, 1994; Simo et al., 2021). The degree of impact of HVL on dose can be defined by the P-value. The statistical results from Table 4 show that the P-value was >0.05 for both cases, implying that HVL had less influence on the dose. Based on these statistical results, we can conclude that dose does not solely depend on HVL, but rather several factors, as referred to in Equation (2) [8] (Poletti, 1994).

Despite the discrepancies in the HVLs discussed in the results and discussion, HVL and kV output follow a normal variation of the linear relationship with HVL increasing with tube potential (kV) [8] [32] - [34] (Ofori et al., 2016; Patel, 1992; Poletti, 1994; Procter, 1973). During our routine inspections, we found out that most machines that failed the kV accuracy test also failed the HVL test. Consequently, the calibration of kV automatically affected the HVL values. Also, [33] (Patel, 1992) noted that the linear relationship of kV and HVL tends to diminish

at high kV values. This was not observed in our study due to a limited range of kV values that were selected. But this is also attributed to the fact that most facilities in Uganda use kV ranges from 50 - 90 kV for justified medical exposures.