Linearity

It is imperative that a properly functioning general X-ray unit produces proportional changes in exposure as milliamperage is changed. The test performed in this lab tests the accuracy of linear output regarding two factors: changes in mAs (with fixed kVp) and reciprocity between mA and exposure time (in seconds).

For the first component of the lab, exposure output (in milliroentgens) was recorded using a radiation meter. Using a fixed kV (70 kV) and starting at 10 mAs, two exposures were taken after approximately doubling the selected mAs until 64 mAs. Exposures were taken at 80 mA on a small focal spot setting and at 160 mA at a large focal spot setting. The lab was conducted in rooms 3 and 6.

Since theoretically, exposure should change proportionately to mAs, the ratio of exposure to mAs (mR/mAs) should be the same for any two sets of exposures at different mAs settings. Both Safety Code 35 and the HARP Act stipulate that the difference in the average mR/mAs values for any two adjacent mA settings must be less than or equal to 10% of the sum of the averages:

|x1 - x2| ≤ 0.10(x1 + x2)

where x1 and x2 are the average mR/mAs (milliroentgens divided by milliampere-seconds) values obtained at the two selected settings of mA (milliamperes)

Tables 1A-D below summarize the results for the first half of the lab in rooms 3 and 6:

Table 1A: Exposure readouts at 80 mA, small focal spot in room 3

80 mA small focal spot	10 mAs	16 mAs	32 mAs	64 mAs
Exposure 1 [mR]	0.083	0.133	0.265	0.529
Exposure 2 [mR]	0.082	0.133	0.265	0.529
Average mR	0.083	0.133	0.265	0.529
mR/mAs (xn)	8.25 x 10-3	8.31 x 10-3	8.28 x 10-3	8.27 x 10-3

Table 1B: Exposure readouts at 160 mA, large focal spot in room 3

160 mA large focal spot	10 mAs	16 mAs	32 mAs	64 mAs
Exposure 1 [mR]	0.086	0.133	0.263	0.523
Exposure 2 [mR]	0.086	0.133	0.263	0.523
Average mR	0.086	0.133	0.263	0.523
mR/mAs (xn)	8.60 x 10-3	8.31 x 10-3	8.22 x 10-3	8.17 x 10-3

Table 1C: Exposure readouts at 80 mA, small focal spot in room 6

80 mA small focal spot	10 mAs	16 mAs	32 mAs	64 mAs
Exposure 1 [mR]	0.098	0.154	0.307	0.605
Exposure 2 [mR]	0.096	0.154	0.306	0.602
Average mR	0.097	0.154	0.307	0.604
mR/mAs (xn)	9.70 x 10-3	9.63 x 10-3	9.58 x 10-3	9.43 x 10-3

Table 1D: Exposure readouts at 160 mA, large focal spot in room 6

160 mA large focal spot	10 mAs	16 mAs	32 mAs	64 mAs
Exposure 1 [mR]	0.095	0.153	0.308	0.608
Exposure 2 [mR]	0.095	0.152	0.308	0.61
Average mR	0.095	0.153	0.308	0.609
mR/mAs (xn)	9.50 x 10-3	9.53 x 10-3	9.63 x 10-3	9.52 x 10-3

Although they show slight variances in mR/mAs, none of the above data for any n demonstrate deviance outside of the accepted limits stated by SC 35 or the HARP Act; hence corrective action is not needed.

The second part of this lab tests for linearity between the reciprocity of mA and exposure time. At a fixed kV (70 kV), mA and exposure time were adjusted so that 16 mAs was always selected for exposure. Two exposures were made for three different mA stations, and the mR/mAs value was calculated. Tables 2A and B below summarize the results for the second half of the lab in rooms 3 and 6:

Table 2A: Exposure readouts for room 3

	80 mA x 0.2 s	160 mA x 0.1 s	320 mA x 0.05 s
Exposure 1 [mR]	0.133	0.133	0.131
Exposure 2 [mR]	0.133	0.133	0.13
Average mR	0.133	0.133	0.131
mR/mAs (xn)	8.31 x 10-3	8.31 x 10-3	8.22 x 10-3

Table 2B: Exposure readouts for room 6

	80 mA x 0.2 s	160 mA x 0.1 s	320 mA x 0.05 s
Exposure 1 [mR]	0.154	0.155	0.148
Exposure 2 [mR]	0.151	0.152	0.149
Average mR	0.153	0.154	0.149
mR/mAs (xn)	9.53 x 10-3	9.59 x 10-3	9.28 x 10-3

These data show even more variance but are still within the accepted limits and hence, corrective actions is also not needed regarding the linearity of mA and exposure time reciprocity.

While control charts are the cornerstone of radiologic quality control, I feel that a different tool can be used to effectively evaluate the linearity of mAs and exposure output. Below is a plot of average exposure [mR] as a function of mAs for the data shown in table 1A:

The line shows the ideal, proportionate change in exposure as mAs is changed, assuming a baseline level at the first exposure. The points around this line are those found in table 1A. Error bars that reflect the acceptable limits in SC 35 and the HARP Act are included. So long as the line is within the error bars of the data points, corrective action is not needed. This method of plotting values against an ideal function can be used as a rapid tool for visually evaluating linearity between exposure and mAs.