Krajowe centrum ochrony radiologicznej w ochronie zdrowia

Doses

DEFINITIONS OF SOME QUANTITIES USED IN MEDICAL X-RAY CLINICS

X-ray tube output, Wd,U:

W_{\scriptscriptstyle d,U}= \frac {K_{\scriptscriptstyle d,U}}{I_{\scriptscriptstyle R} \cdot t}

where: Kd,U – is the air kerma measured on the central beam axis at distance d from x-ray tube focus for voltage U, IR∙t – is tube-current exposure-time product. In the SI system x-ray tube output is expressed in units of [Gy/C] or [Gy/A·s], usually the tube output is expressed in units of [mGy/mA·s].

Kerma-area product, KAP:

\textit{KAP}=\int_A K_a ~ dA

simplified formula: KAP=Ka*A

where: Ka – is the air kerma measured on area A. In the SI system, the air kerma-area product is usually expressed in units of [Gy·m2]. For x-ray radiation KAP is equivalent of DAP (dose-area product).

Kerma-length product DLP:

\textit{DLP} = \int_L D \left ( z \right )~dz

where: D(z) – is the absorbed dose distribution alongside the axis of rotation of a CT scanner (z-axis) for a single rotation of a CT scanner (360˚). In the SI system, DLP is expressed in units of [Gy·m].

Computed tomography dose index, CTDI100:

\textit{CTDI}_{\scriptscriptstyle {100}} = \frac 1 {N \cdot s} \int^{+50 mm}_{-50 mm} D \left ( z \right )~dz

where: D(z) – is the absorbed dose distribution alongside the axis of rotation of a CT scanner  (z-axis) for a single rotation of a CT scanner (360˚), s – nominal slice thickness, N – number of slices per single rotation. In the SI system CTDI100 is expressed in units of [Gy].

Weighted CT dose index, CTDIw:

\textcolor{black}{\textit{CTDI}_w = \frac 1 3 \textit{CTDI}_{100,A} + \frac 2 3 \textit{CTDI}_{100,P}} (fantomy PMMA);

where: A – is the axis of rotation of a scanner, P – 10 mm slice thickness from the surface of the phantom. In the SI system, CTDIw is expressed in units of [Gy].

CT pitch factor, CTPF:

\textit{CTPF} = \frac {\varDelta d} {N \cdot s}

where: Δd – is the distance moved by the patient coach per a single rotation of the scanner, N, s – see above. CTPF is a dimensionless quantity.

Volume averaged weighted CT dose index, CTDIvol:

\textit{CTDI}_{vol} = \frac {\textit{CTDI}_w} {\textit{CTPF}}

In the SI system, CTDIvol is expressed in units of [Gy].

\textit{DLP} = \textit{CTDI}_{vol} \cdot L

where: L – total scan length during the examination

Entrance surface dose, Dent:

D_{\scriptscriptstyle ent} = K_{\scriptscriptstyle E} \cdot B

where: KE – is air kerma measured at the surface of patient’s skin where the beam enters the patient, B – backscatter radiation from the patient. In the SI system, Dent is expressed in units of [Gy].

Table 1: Rough estimates of backscatter factor for the voltage around 70 kV depending on filtration an beam field size (on the basis of IAEA training materials)

HVL

Beam field size (cmxcm)

mm Al

10 x 10

15 x 15

20 x 20

25 x 25

30 x30

2,0

1,26

1,28

1,29

1,30

1,30

2,5

1,28

1,31

1,32

1,33

1,34

3,0

1,30

1,33

1,35

1,36

1,37

4,0

1,32

1,37

1,39

1,40

1,41

Entrance skin dose, ESD:

\textit{ESD} = K_{\scriptscriptstyle E} \cdot B \left ( \frac \mu \rho \right )^{skin}_{air}

where KE – is air kerma measured at the beam axis on the patient’s skin, B – backscatter factor from the patient, (μ/ρ) – mass absorption coefficient skin-to-air. In the SI system, ESD is measured in units of [Gy].

Table 2: Mass absorption coefficient for skin, air and skin-to-air for selected voltages (on the basis of ICRU-44 and J.H Hubbell and S. M. Seltzer)

Energia [keV]

\textcolor{black}{\left ( \frac \mu \rho \right )^{skin}}

\textcolor{black}{\left ( \frac \mu \rho \right )_{air}}

\textcolor{black}{\left ( \frac \mu \rho \right )_{air}^{skin}}

50

0,2264

0,2080

1,0885

60

0,2048

0,1875

1,0923

80

0,1823

0,1662

1,0969

100

0,1693

0,1541

1,0986

150

0,1492

0,1356

1,1003

RELATIONSHIPS BETWEEN SOME QUANTITIES USED IN X-RAY CLINICS

Relationship between kerma (dose) and distance:

K_{\scriptscriptstyle 1} = K_{\scriptscriptstyle 2} \left ( \frac {r_{\scriptscriptstyle 2}} {r_{\scriptscriptstyle 1}} \right )^2

where: ri – is the distance from the tube focus, Ki – is the air kerma (dose) at distance ri

Relationship between kerma and kerma-area product (KAP):

K_{\scriptscriptstyle S} = \frac {\textit{KAP}} {A_{\scriptscriptstyle S}}

where: KAP – is the measured kerma-area product, AS – radiation field in the plane perpendicular to the beam axis at point S, KS – kerma at point S. For x-ray radiation KAP is equivalent to DAP.

Relationship between beam field sizes:

A_{\scriptscriptstyle 1} = A_{\scriptscriptstyle 2} \left ( \frac {r_{\scriptscriptstyle 1}} {r_{\scriptscriptstyle 2}} \right )^2

where: ri – is the distance from the tube focus, Ai – beam field size at distance ri

Calculating kerma at point E based on measured tube output:

K_{\scriptscriptstyle E}  = W_{\scriptscriptstyle d,U} \cdot I_{\scriptscriptstyle R} \cdot t \cdot \left ( \frac {r_{\scriptscriptstyle d}} {r_{\scriptscriptstyle E}} \right )^2

where: Wd,U – is the tube output calculated in point d for voltage U, IR·t – is the tube-current exposure-time product, rd –  distance between the point where output was measured, Wd,U, and the tube focus, rE – distance of the point where kerma KE  was determined from the tube focus.

GENERAL ALGORITHM FOR CALCULATING ENTRANCE SURFACE DOSE AND ENTRANCE SKIN DOSE

Simplified calculations:

For more information see:

  1. H. Aichinger, J. Dierker, S Joite-Barfuss, M.Saebel: Radiation Exposure and Image Quality in X-ray Diagnostic Radiology (Springer 2004, ISBN 3-540-44287-1) link
  2. Entrance skin dose estimates derived from dose-area product measurements in interventional radiological procedures, B. J. McParland, BJR, 71 (1998), 1288 – 1295 link
  3. A study of patient radiation doses in interventional radiological procedures B.J. McParland, BJR, 74 (2001), 727 – 734 link
  4. Differences in effective dose estimation from dose-area product and entrance surface dose measurements in intravenous urography E. Yakoumakis at al, BJR,, 74 (2001), 920 – 925 link
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