Radiological Physics and Technology https://doi.org/10.1007/s12194-018-0457-2

(0123456789().,-volV)(0123456789().,-volV)

Body size and tube voltage-dependent guiding equations for optimal selection of image acquisition parameters in clinical X-ray imaging Xiaoming Zheng1 Received: 17 January 2018 / Revised: 31 March 2018 / Accepted: 11 April 2018 Ó Japanese Society of Radiological Technology and Japan Society of Medical Physics 2018

Abstract The purpose of this work was to present body size and tube voltage-dependent equations for optimal selection of image acquisition parameters in guiding clinical X-ray imaging. The dose output of X-ray tubes was expressed as a function of the image acquisition parameters of tube voltage (kVp), tube current–exposure time product (mAs), and body size (d). Dose power (n) to kVp was determined to be a linear function of body size in an earlier phantom study. Tube voltage-dependent attenuation coefficients of water were used to determine the kVp effect on the depth dose of X-rays from the body’s entrance surface. The new expression for the dose output of X-ray tubes in patients was then employed for image quality and radiation dose optimization, assuming that image quality is a logistic function of the radiation dose to patients. For constant kVp, the percentage of mAs increase for a 1-cm increase in body size d is dependent on the kVp applied. For constant mAs, the percentage of kVp increase for a 1-cm increase in body size is dependent on both body size d and the kVp applied. For constant body size, the percentage of kVp increase should be a fraction of the percentage of decrease in the mAs, where the fraction is dependent on the body size. The improved body size and tube voltage-dependent governing equations for variations in X-ray imaging parameters should be more accurate in guiding optimal selection of the kVp and mAs image acquisition parameters in medical X-ray imaging. Keywords X-ray imaging  Computed tomography  Radiographic imaging  Imaging acquisition parameters  Guiding equations

1 Introduction Achieving adequate image quality for patient diagnosis and the lowest possible radiation dose received by patients is one of the major objectives in medical X-ray imaging, including computed tomography (CT) and radiographic imaging (i.e., computed or digital radiography) [1]. Minimizing radiation dose to patients while achieving targeted clinical outcomes is not only desirable for patient wellbeing, but also for technical reasons, such as reducing the load on and increasing the life expectancy of X-ray tubes [2]. Both image quality and radiation dose to patients are dependent on numerous image acquisition parameters, such & Xiaoming Zheng [email protected] 1

Medical Radiation Science, School of Dentistry and Health Sciences, Faculty of Science, Charles Sturt University, Wagga Wagga, NSW 2678, Australia

as X-ray tube voltage peak (kVp) and tube current–exposure time product (mAs). Optimal selection of these image acquisition parameters is critical in clinical X-ray imaging practice [1]. In radiographic imaging, manufacturers generally recommend kVp and mAs for each anatomical region or clinical indication. The recommended kVp and mAs can be adjusted according to a patient’s body size using tables, charts, or ‘‘rules of thumb’’ [3, 4]. These rules of thumb are based on trial and error, and different radiographers may prescribe vastly different exposures for the same patient. To ensure the safety of the minimum dose received by patients, the current international standard sets a target ‘‘exposure index’’ in guiding clinical practice [5]. This target exposure index is based on the exposure of a detector, not the dose received by patients, which is the main health concern. Furthermore, a higher tube voltage is recommended for specific anatomic regions [1, 6] and a 15% rule of thumb: for a 15% increase of kVp, half the

X. Zheng

mAs is recommended in determining the required mAs reduction [6]. In X-ray CT imaging, manufacturers also recommend kVp and mAs for each of the anatomical regions as well as tables or charts for various body sizes. To minimize the radiation dose received by patients, automatic exposure control [7] and automated tube voltage selection [8] are employed during CT data acquisition. These techniques use projection angle-dependent kVp and mAs to reduce the radiation dose received by patients while maintaining constant image quality using either an image noise index or contrast-to-noise ratio [7, 8]. These image quality indices are useful physical image quality parameters but their accuracy is insufficient for diagnosis because diagnostic image quality requires a human observer and is dependent on the clinical task. Furthermore, a lower tube voltage is recommended for CT imaging in children, but no guidance exists in the literature on how the mAs should be adjusted in response to the reduced kVp [9]. Recently, Zheng [10–12] derived several equations for optimal selection of kVp and mAs as image acquisition parameters in clinical X-ray imaging, including CT and radiographic imaging. The derivations of these equations were based on well-known formulae for the dose output of X-ray tubes and experimentally demonstrated relationships between diagnostic image quality and the radiation dose to patients [12]. Body size was accounted for by employing experimentally measured body sizespecific dose correction factors [11, 13]. Two parameters, the exponent n of kVp and parameter c of the sizespecific dose correction factor, were assumed to be imaging system and protocol-dependent constants [10–12]. The parameter c used in these equation derivations for CT was measured with a kVp of 120 [13] and, for radiographic imaging, c was an averaged kVp of 80 and 100 [11]. Parameter c was expected to be kVpdependent [11]. More recently, Zheng et al. [14] found that the power n of kVp in phantoms is a linear function of body size. These findings suggest that the well-known expression for determining the dose output in phantoms (patients) from X-ray tubes should be revised. The

purpose of this work was to examine the effect of the dose power n as a linear function of body size on the formula for determining the dose output in phantoms (patients) from X-ray tubes and, in turn, its effect on the general equations for optimal selection of image acquisition parameters in clinical X-ray imaging, including CT and radiographic imaging.

2 Methodology The methodology employed in this work is the same as that employed in previous studies [10–12]. Assuming image quality Qi is a function of radiation dose D, Q i ¼ f ðD Þ

ð1Þ

The mathematical condition for a maximum Qi is DQi ¼ 0:

ð2Þ

Because image quality is a monotonic function of radiation dose to phantoms (patients), a dose efficiency index can be defined as Ed ¼

DQi ; DD

ð3Þ

and for maximum radiation dose efficiency Ed ; the mathematical condition is DEd ¼ 0:

ð4Þ

The radiation dose to phantoms (patients), assuming all other imaging parameters are fixed, is generally expressed as follows [10–12]:   D As ; Vp ; r ¼ KAs Vpn ecd ; ð5Þ where K is a constant, As is the tube–current time product or mAs, Vp is the tube voltage kVp, d is the patient body thickness, n is the dose power, and c is a constant for the size-specific dose correction factor [10–12]. Both n and c were assumed to be imaging system and protocol-dependent. More recently, the dose power n at the center of the body (phantom) or at depth r from the entrance surface of the X-rays was found to be a linear function of body size or depth distance r from the entrance surface [14]:

Body size and tube voltage-dependent guiding equations for optimal selection of image acquisition...

nðr Þ ¼ ar þ b;

ð6Þ

where a and b are two constants and r = d/2 is the radius of the body or depth distance from the entrance surface of the X-rays. Theoretical calculations using kVp-dependent attenuation coefficients of water revealed a = 0.0619 and b = 2, and dose measurements of CT phantoms were averaged as a = 0.068 and b = 2.05 [14]. On the basis of Eq. (6), showing that the dose power n is a linear function of body size, Eq. (5) may be revised as     D As ; Vp ; r ¼ KAs Vparþb f Vp ; r ; ð7Þ   where f Vp ; r is a kVp and body size r = d/2-dependent function that must be determined. Using a water absorber to approximate the dose to patients, the radiation output of radiographic imaging at depth distance r from the entrance surface of the X-rays can be expressed as     D As ; Vp ; r ¼ KAs Vparþb f Vp ; r ¼ KAs elðVp Þr ; ð8Þ or   elðVp Þr f Vp ; r ¼ arþb ; ð9Þ Vp   where l Vp is a kVp-dependent attenuation coefficient. For the water absorber, employing the kVp-dependent   attenuation coefficients of l Vp ¼ 0:2059; 0:1837; 0:1707 for Vp = 60, 80, 100 [15] and a and b values calculated from the same kVp-dependent attenuation coefficients, the   f Vp ; r can be determined to be   f Vp ; r ¼ e½0:53560:018lnðVp Þr : ð10Þ For CT imaging, no similar kVp-dependent attenuation coefficients exist, as they do for the aforementioned radiographic imaging. Assuming that X-rays pass through a patient twice in opposite directions during CT image acquisition, as stated in Ref. [14], the kVp-dependent attenuation coefficients for CT may be determined using the aforementioned kVp-dependent attenuation coefficients   of water. Thus, the same f Vp ; r can be determined to be   f Vp ; r ¼ e½0:53020:023lnðVp Þr : ð11Þ Equation (11) suggests that the kVp-dependent attenuation coefficients for CT are only slightly lower than those

for radiographic projection X-ray imaging. A general   equation of f Vp ; r for both radiographic imaging (Eq. 10) and CT (Eq. 11) can be expressed as   ð12Þ f Vp ; r ¼ e½srlnðVp Þr ; where r and s are two constants, as shown in Eqs. (10) and (11). Equation (7) now becomes   d adþb D As ; Vp ; d ¼ KAs Vp 2 e½srlnðVp Þ2 ; ð13Þ or   d n ðd Þ D As ; Vp ; d ¼ KAs Vp 2 ehðVp Þ2 ;

ð14Þ

where     h Vp ¼ s  rln Vp :

ð15Þ

Equation (15) suggests that the assumed constant h in Ref. [14] is dependent on the applied tube voltage kVp. Diagnostic image quality may be expressed as a general logistic function of radiation dose to patients, as demonstrated in Ref. [12]: Qi ðDÞ ¼

C ; 1 þ BexD

ð16Þ

where B, C, and x are three constants that accommodate various forms and shapes of the logistic function found in clinical imaging.

3 Results Employing Eqs. (16), (3) becomes  2   DQi Ed ¼ ¼ C 1 þ BexD BxexD DD BCxexD : ¼ ð1 þ BexD Þ2

ð17Þ

Employing Eqs. (13), (17) becomes DQi ¼ Ed ¼ DD

ad þb ½srlnðVp Þd 2 e 2

AexKAs Vp 1þ

adþb ½srlnðVp Þd 2 e

2 BexKAs Vp

2 ;

ð18Þ

where A = BCx is a constant. Equation (4) now becomes

X. Zheng

      oEd As ; Vp ; d oEd As ; Vp ; d oEd As ; Vp ; d DEd ¼ DAs þ DVp þ Dd oAs oVp od 2 3 2 3 d d adþb 6 7 BexKAs Vpa2þb e½sr lnðVp Þd2  1 xKAs Vp 2 e½sr lnðVp Þ2 Ae 6 7 5 ¼ 6 2 74 d ad þb 4 5 ad þb ½sr lnðVp Þd xKAs Vp 2 e½sr lnðVp Þ2 þ 1 2 e 2 xKA V Be s p 1 þ Be h iDA  ad2þb ½sr lnðVp Þd s 2 xKAs Vp e As 2 3 2 3 d d a þb ½sr lnðVp Þd 2 6 7 BexKAs Vpa2þb e½sr lnðVp Þd2  1 2 AexKAs Vp e 6 74 5 þ 6 2 7 adþb ½sr lnðVp Þd 4 5 ad þb ½sr lnðVp Þd 2 e 2 xKA V 2 e s p 2 xKA V þ1 Be s p 1 þ Be    i d d DVp a þb þr 2 2 Vp 3 2 3 d d adþb 6 7 BexKAs Vpa2þb e½sr lnðVp Þd2  1 xKAs Vp 2 e½sr lnðVp Þ2 Ae 6 7 5 þ 6 2 74 adþb ½sr lnðVp Þd 4 5 ad þb ½sr lnðVp Þd 2 e 2 xKA V 2 s p 2 þ1 Be 1 þ BexKAs Vp e h

adþb

xKAs Vp 2 e½sr lnðVp Þ2 2 d

ð19Þ

i1      a ln Vp  s  r ln Vp Dd 2 2 3 2 3 d adþb ½sr lnðVp Þd ad þb 6 7 2 xKAs Vp 2 e xKAs Vp 2 e½sr lnðVp Þ2 Ae  15 6 7 Be ¼ 6 2 74 ad þb ½sr lnðVp Þd 4 5 ad þb ½sr lnðVp Þd 2 2 2 2 þ1 BexKAs Vp e 1 þ BexKAs Vp e h

d adþb xKAs Vp 2 e½sr lnðVp Þ2

h

i d adþb xKAs Vp 2 e½sr lnðVp Þ2   

   DAs d d DVp 1    þ a þb þr þ a ln Vp  s þ r ln Vp Dd ¼ 0; 2 2 Vp 2 As

or

or

      DAs d 1 DVp 1    þ n  h Vp  aln Vp Dd þ rd 2 2 2 As Vp ¼ 0:

  DAs ¼ c Vp Dd; As ð20Þ

Equation (20) is the general constraint equation for the variations of kVp, mAs, and body size d. The same equation can be derived by assuming that diagnostic image quality is a logarithmic or linear function of radiation dose, as stated in Ref. [12]. Given a constant tube voltage kVp, Eq. (20) becomes   DAs 1    ð21Þ ¼ h Vp  aln Vp Dd; 2 As

ð22Þ

where   1     c Vp ¼ h Vp  aln Vp : 2 Given a constant mAs, Eq. (20) becomes "      # 1 DVp 2 h Vp  aln Vp ¼ Dd; Vp n d2 þ 12 rd or

ð23Þ

ð24Þ

Body size and tube voltage-dependent guiding equations for optimal selection of image acquisition... Table 1 Calculated percentage of mAs increase per 1-cm body size increase, c, at various kVp values

Tube voltage, kVp Radiographic imaging, Computed tomography,

  DVp c Vp ¼ Dd; Vp m ðd Þ

DAs As DAs As

ð25Þ

where mðd Þ ¼ n

  d 1 þ rd; 2 2

Given a constant body size d, Eq. (20) becomes     DAs d 1 DVp ¼ n ; þ rd 2 2 As Vp

ð26Þ

ð27Þ

or DAs DVp ¼ mðd Þ : As Vp

ð28Þ

Equations (22), (25), and (28) are the revised general equations of Eqs. (19), (20), and (21) in Ref. [12], respectively.

4 Discussion Given a constant kVp, Eq. (22) is the guiding equation for the percentage of mAs increase if body size d is increased by 1 cm. Equation (22) is the same as Eq. (19) in Ref. [12], except that c is now a function of the applied kVp (Eq. 23). The parameter c in References [10–12] is a constant of the size-specific dose correction factor. For CT imaging, c = 0.038 is the average of adults (d = 32 cm) and children (d = 16 cm) that was measured at a kVp of 120 [13]. For radiographic imaging, c = 0.078 was the averaged value of kVp = 80 and 100 [11]. Equation (23) shows that the sizespecific dose correction factor c is kVp-dependent, which is consistent with Ref. [11]. The kVp-dependent c values can be calculated using Eq. (23), as shown in Table 1. For radiographic imaging at kVp = 80 and 100, the calculated c values are c = 0.083 and 0.074, as shown in Table 1, which are in excellent agreement with the experimentally determined values of c = 0.083 and 0.073 [11], averaged as c = 0.078. As previously discussed, the c value is the percentage of mAs increase per 1-cm body diameter increase in plain radiographic X-ray imaging or automatic exposure control in X-ray fluoroscopic imaging [11, 12]. Table 1 shows that a slightly higher percentage of mAs increase should be applied if the applied kVp is reduced. Table 1 shows an average 7.86% mAs increase per 1-cm body diameter increase for radiographic imaging.

60

70

80

90

100

110

120

0.095

0.086

0.083

0.078

0.074

0.069

0.065

0.082

0.075

0.069

0.064

0.059

0.055

0.051

This is consistent with the 7.8% mAs increase calculated in Ref. [11], but is approximately half of the 15% mAs increase per 1-cm body size increase employed in current clinical practice [17]. It represents a considerable dose reduction from the current level without compromising the accuracy of patient diagnosis in radiographic imaging. A recent clinical study confirmed the aforementioned equations and dose reductions [18]. For CT imaging, the c value was determined to be 0.037 for adults and 0.039 for children at a kVp of 120 [13]. These values were derived from the best fit curves of the CT dose index (CTDIv) versus body size. The CTDIv is an averaged CT dose index and our dose measurements suggested that doses measured at the center of phantoms are more accurate than the averaged CTDIv [14]. If the CT dose is normalized to the phantom’s center [16], c is estimated to be 0.047 [14], which is close to the value of 0.051 at kVp = 120, as shown in Table 1. Notably, the kVp-dependent attenuation coefficients for CT were estimated from the X-rays assumed to be passing through the body in the opposite direction during a CT scan, which is only an approximation. Nevertheless, Table 1 shows that it is a reliable approximation. Ideally, these kVp-dependent attenuation coefficients should be measured experimentally in the same manner as those for radiographic imaging. Equation (22) is the guiding equation for automatic mAs control in CT imaging, and the variations of mAs per 1-cm body thickness increase are dependent on the kVp applied, as in radiographic imaging. The only difference is that a slightly smaller mAs increase per 1-cm body thickness increase is required for CT than that for radiographic imaging. Given a constant mAs, Eq. (25) is the guiding equation for optimal kVp selection or automatic kVp control in both CT and radiographic imaging. Equation (25) suggests that the percentage of kVp increase is dependent on both body size d and the kVp applied, which is more complicated than that for the aforementioned automatic exposure mAs control. For averaged adults (d = 32 cm) and children (d = 16 cm), the calculated percentages of kVp increase per 1-cm increases in body size at various kVp values are listed in Table 2. For radiographic imaging, Table 2 gives a

DVp Vp

increase

of 0.0229 for adults averaged at kVp = 80 and 100, which mirrors the value of 0.023 in the experimental data [11]. The overall values are approximately 2–3% (Table 2).

X. Zheng Table 2 Calculated percentage of kVp increase per 1-cm increase in body size d of adults (d = 32 cm) and children (d = 16 cm), given a constant mAs

Table 3 Calculated percentage of mAs increase for various percentages of kVp decrease for adults (d = 32 cm) and children (d = 16 cm)

KVp

Radiographic imaging DVp Vp

(d = 32 cm)

Computed tomography DVp Vp

(d = 16 cm)

DVp Vp

(d = 32 cm)

DVp Vp

(d = 16 cm)

60

0.0277

0.0347

0.0234

0.0295

70

0.0251

0.0314

0.0214

0.0270

80

0.0242

0.0303

0.0197

0.0248

90

0.0228

0.0285

0.0183

0.0230

100

0.0216

0.0270

0.0168

0.0212

110

0.0201

0.0252

0.0157

0.0198

120

0.0190

0.0237

0.0145

0.0184

DAs As

DAs As



DVp Vp

Radiographic imaging DAs As

(d = 32 cm)

Computed tomography (d = 16 cm)

(d = 32 cm)

DAs As

(d = 16 cm)

0.05

0.1713

0.1369

0.1753

0.1389

0.10

0.3246

0.2738

0.3506

0.2778

0.15

0.5139

0.4107

0.5259

0.4167

0.20

0.6852

0.5476

0.7012

0.5556

0.25

0.8565

0.6845

0.8765

0.6945

0.30

1.0278

0.8214

1.0518

0.8334

Table 2 shows that at kVp = 100, the kVp increase is 2.16 kV/cm for an adult, which is consistent with the 2-kV/ cm rule of thumb used in clinical practice [3]. Table 2 shows that this 2-kVp/cm rule should be slightly adjusted according to the kVp applied and the body size. Although this was expected [3, 4], no guidance exists in the literature. A slightly higher percentage of kVp increase should be applied to adult patients and when the kVp value is lower (Table 2). On average, the 2-kV/cm rule of thumb is a reliable approximation. For CT imaging of an average adult at 120 kVp, Table 2 shows a 1.45% increase per 1-cm increase in body size which is close to the average value of 1.53% in Ref. [10]. Equation (25) is thus the body size and kVp-based automatic kVp control for CT, which contrasts with the attenuation-based tube voltage selection in CT [8]. The implementation of both body size-based automatic kVp and mAs controls for CT was described in a recent Australian patent [19]. Given a constant body size d, Eq. (28) suggests that the percentage of mAs increase in response to the percentage of kVp decrease is dependent on body size d. For radiographic imaging, the percentage of mAs increase should be 3.426 and 2.738 times the percentage of kVp decreases for adults (d = 32 cm) and children (d = 16 cm), respectively. For CT imaging, the percentage of mAs increase should be 3.506 and 2.778 times the percentage of kVp decrease for adults (d = 32 cm) and children (d = 16 cm), respectively. Table 3 shows the calculated percentage of mAs increase

for various percentages of kVp decrease for adults and children. For CT imaging, numerous studies have suggested that a standard of 120 kVp may be used for adult CT imaging but a lower kVp, such as 90 kVp, should be employed for children [9]. A lower kVp dramatically reduces the dose to patients at the same mAs, but also increases image noise considerably. An increase in mAs is generally required to compensate for the increased image noise to maintain diagnostic image quality. However, no guidance exists in the literature on the mAs increase that should be applied for specific kVp reductions [9]. Hence, Eq. (28) is a guiding equation derived for this purpose. Furthermore, Table 3 shows that the mAs increase for children should be lower than that for adults for the same percentage of kVp decrease. For example, if the kVp is lowered by 25% from 120 to 90 kVp, the mAs increase for an adult is 87.65%, whereas an increase of only 69.45% is needed for CT imaging in children. This is another reason why a lower kVp should be employed for CT imaging in children. For radiographic imaging, the 15% rule of thumb states that, for a 15% increase in kVp, the mAs should be halved [3, 4]. Table 3 shows that, for a 15% kVp increase, the mAs should be reduced by 51.4% for adults (d = 32 cm), which closely adheres to the 15% rule of thumb. However, for children, the mAs decrease should be 41.1%, which is less than that for adults if the kVp is increased by 15%. This suggests that an increased kVp is disadvantageous for radiographic imaging of children, or a lower kVp should be

Body size and tube voltage-dependent guiding equations for optimal selection of image acquisition...

applied for children in radiographic imaging, as in the aforementioned CT imaging. This is consistent with the European Commission’s guidelines for radiographic imaging of children [20]. Finally, future experimental measurements of kVp-dependent attenuation coefficients for CT are warranted because the calculated values appear to have slightly underestimated the effect of kVp on the attenuations in CT imaging.

5 Conclusion X-ray tube voltage and patient body size-dependent guiding equations were derived for optimal selection of image acquisition parameters in clinical X-ray imaging, including CT and radiographic imaging. These are revised general equations that incorporate more accurate expressions of the dose output of X-ray tubes received by patients (phantoms) as a function of image acquisition parameters, and thus are more accurate in guiding clinical practice. Implementing these governing equations in medical X-ray imaging can reduce the radiation dose received by patients. Acknowledgements I would like to thank the Journal Editor for English editorial assistance and my colleague Mr. Andrew Kilgour for critical reading of and comments on this manuscript.

Compliance with ethical standards Conflict of interest The author declares that there is no conflict of interest in this work. Research involving human or animal participants This article does not report any studies involving human participants or animals performed by the author. Informed consent Informed consent is not required.

References 1. Huda W, Abrahams RB. Radiographic techniques, contrast, and noise in X-ray imaging. AJR. 2015;204:W126–31. 2. Kalender WA, Wolf K, Suess C. Dose reduction in CT by anatomically adapted tube current modulation. II. Phantom measurements. Med Phy. 1999;26(11):2248–53. 3. Ching W, Robinson J, McEntee M. Patient-based radiographic exposure factor selection: a systematic review. J Med Rad Sci. 2014;61:176–90.

4. Van der Plaats GJ. Medical X-ray techniques in diagnostic radiology. London: The Macmillan Press Ltd; 1980. 5. AAPM task group 116. An exposure indicator for digital radiography. College Park: American association of physicists in medicine; 2009. ISBN 978-1-888340-86-0. 6. Herrmann TL, Fauber TL, Gill J, Hoffman C, Orth DK, Peterson PA, Prouty RR, Woodward AP, Odle TG. Best practices in digital radiography. Radiol Technol. 2012;84:83–9. 7. Soderberg M, Gunnarsson M. Automatic exposure control in computed tomography—an evaluation of system from different manufacturers. Acta Radiol. 2010;6:625–34. 8. Spearman JV, Schoepf UJ, Rottenkolber M, Driesser I, Canstein C, Thierfelder KM, Krazinski AW, De Cecco CN, Meinel FG. Effect of Automated attenuation-based tube voltage selection on radiation dose at CT: an observational study on a global scale. Radiology. 2016;279(1):167–74. 9. Wambersie A. Radiation quantities and units, dose to the patients, and image quality in computed tomography (CT). European Commission Directorate-General for Research; EUR 23464; 2008. https://www.cordiseuropa.eu/project/rcn/75837_en.html. Accessed 16 Apr 2018. 10. Zheng X. Attenuation based governing equations for automatic mAs and kVp controls in medical X-ray CT imaging. CT Theory Appl. 2016;25(6):625–32. 11. Zheng X. Patient size based guiding equations for automatic mAs and kVp selections in general medical X-ray projection radiography. Radiat Prot Dosim. 2017;174(4):545–50. 12. Zheng X. General equations for optimal selection of diagnostic image acquisition parameters in clinical X-ray imaging. Radiol Phys Technol. 2017;10:415–21. 13. AAPM task group 204. Size-specific dose estimates (SSDE) in paediatric and adult body CT examinations. College Park: American association of physicists in medicine; 2011. ISBN 978-1-936366-08-8. 14. Zheng X, Nardi L, Murray M. Size effect on dose output in phantoms of X-ray tubes in medical X-ray imaging. Biomed Phys Eng Express. 2017;3:065004. 15. NIST (n, d) X-ray mass attenuation coefficients—water, liquid. https://physics.nist.gov/PhysRefData/XrayMassCoef/ComTab/ water.html. Accessed 26 Sep 2017. 16. ICRU Radiation dose and image quality assessment in computed tomography. J ICRU 12 (2012) report 87. 17. Williams MB, Krupinski EA, Strauss KJ, Breeden WK, Rzeszotarski MS. Digital radiography image quality: image acquisition. J Am Coll Radiol. 2007;4:37–88. 18. Zheng X, Chiang H-W, Li J-H, Chiang H-J, Lin L-H. Personal exposure prescription method reducesdose in radiography. Radiol Technol 2018;89(5) (In press). 19. Zheng, X. A method and system for automating radiation dose parameters. Australian patent: AU2016902943. 27-07-2016. 20. European commission. European guideline on quality criteria for diagnostic radiographic images in paediatrics. Luxemburg: Office for official publications of the European communities; 1996. ISBN 92-827-7843-6.