### Introduction

The
operational process of clinical CT imaging is supported by a patient -
technology - observers system with specific interactions of several
factors (e.g. attributes of patient, x ray spectrum and its modulation,
reconstruction algorithms and image quality perception) [1],
affecting dosimetric and image quality quantities. Knowledge of
quantitative association between CT dosimetric and image quality
quantities with systemic factors, constitutes the basis to devise
scanner-specific optimization strategies. Most of CT dosimetric
quantities are derived from CT air kerma index (*C*
_{
pmma,c
} at the center and *C*
_{
pmma,p
} at the perifery) [2]. The aim was to
analyze the association of the air kerma index with systemic factors and
pixel noise, to get insight for specific optimization strategies.

### Materials and methods

Kerma indexes (*C*
_{
a,100
} and *C*
_{
pmma,x
} ) [2] were measured with a pencil ionization chamber (PTW-Freiburg, model TN30009-0577, 3,14 cm^{3}),
and an electrometer Unidos E (PTW-Freiburg) on both standard circular
cylindrical PMMA phantoms with radius of 8 and 16 cm. A systemic
approach was considered [1], regarding the following factors from a CT unit Siemens Sensation 64 Cardiac:

tube current x time product

*F*_{ 1 }(40 - 350 mAs), total collimation projected at isocenter*F*_{ 3 }(2,7 - 19,2 mm), slice thickness*F*_{ 7 }(0,15 - 1 cm), tube potential*F*_{ 8 }(80 and 140 kV), andthe impinging spectrum

*Φ*0 was estimated with SPEKTR 3.0 [3] at the exit of the x ray tube, with added thickness of 0,2; 0,25 and 0,3 mmCu, considering beam qualities as RQT 8 for measurements with 80 kV and 100 kV, RQT 9 for 120 kV and RQT 10 for 140 kV [2], respectively. The attenuated spectrum*Φ*was computed for every phantom diameters and combinations of operational factors used for measurements. Additionally, the Φo and Φ were attenuated with specific inherent filtration, the latter computed using the MATLAB function*spektrTuner*[3], in order to satisfy the measured*C*_{ a,100 }and*C*_{ pmma,c }. For the estimation of attenuated spectrums, the phantom radius was considered as a layer thickness, traversed by all incident photons summed during one rotation of the x ray tube, but with fixed position of the x ray tube.

As *C*
_{
pmma,c
} and *C*
_{
pmma,p
} were measured in PMMA phantoms, and pixel noise measured in water
phantoms, it is convenient to estimate the water equivalent radius *R*
_{
w
} , which is here the thickness of a water layer that produces the
same exposure attenuation that the PMMA layer under the same technical
conditions (tube potential, tube current, collimation, and filtration).

It is very important that the uncertainty associated with the measurements be known and small. Through this work the measurement uncertainties express the 95 % confidence limits of the results, in case of used coverage factor k = 2 will be addressed.

Average pixel noise *σ*
was estimated from measurements with ROIs of 30 x 30 pixels in five
positions (center, 12h, 3h, 6h and 9h) inside images of water phantoms
with radius of 2,5; 3; 6; 8 and 11,5 cm. The same water phantoms were
used in a previous work [4].

Data analysis was the departure to get insight for optimization alternatives. The association between *C*
_{
pmma,c
} and *C*
_{
pmma,p
} was verified graphically and with linear regression analysis. The association of *C*
_{
pmma,c
} with *F*
_{
1
} , *F*
_{
3
} and *σ* was verified with nonlinear regression analysis, with fixed values of tube potential and phantom radius.

### Results and discussion

The expanded uncertainties of *C*
_{
a,100
} and *C*
_{
pmma,c
} were 10,8 % and 12,4 % (k=2) respectively (see details in table 1).

Table 1.

Uncertainty budget for direct measurement of *C*
_{
pmma,p
} and *C*
_{
pmma,c
} using the ionization chamber - electrometer system (i.c.- e)

^{1} SSDL - Secondary Standard Dosimetry Laboratory.

The total fluences were derived with spectrums obtained for all observations (see sample in figure 1 a), and each *R*
_{
w,i
} was computed, corresponding to combinations of PMMA phantom radius and scanning factors *F*
_{
1
} , *F*
_{
3
} and *F*
_{
8
} . For PMMA layers of 8 cm and 16 cm the *R*
_{
w
} were 8,3 ± 0,21 cm and 17,4 ± 0,26 cm respectively.

The quantity *C*
_{
vol
}[2], wich takes into account the helical pitch or axial scan spacing, is linearly associated with *C*
_{
pmma,c
} . Also a linear association was found here between measured *C*
_{
pmma,p
} and *C*
_{
pmma,c
} (see figure 1b).

Figure 1.

(a) Computed tungsten 80kVp spectrum: incident Φ0 (which satisfies *C*
_{
a,100
} ), spectrum Φ that satisfies measured *C*
_{
pmma,c
} , spectrum of primary radiation Φp (Φ0 attenuated with *R*
_{
pmma
} ) and spectrum of scattered radiation Φs (Φ - Φp ). (b) Linear association of *C*
_{
pmma,p
} with *C*
_{
pmma,c
} .

A good agreement between *C*
_{
pmma,p
} and *C*
_{
pmma,c
} was found for both phantom diameters of 8 cm and 16 cm,
represented by the linear regression models y@8 and y@16 respectively in
figure 1b.

The figure 2 a confirms that *C*
_{
pmma,c
} has a direct linear association with *F*
_{
1
} and is inversely proportional to *F*
_{
3
} . Specifically for this example, the steeped surface for *R*
_{
pmma
} = 8 cm allows to identify, quantitatively, the operational
regions with lower doses for pediatric examinations at 80 kV (e.g., less
than 100 mAs and more than 10 mm of total collimation). In figure 2 b is represented the association of mean pixel noise σ with kerma at the center of a water phantom *C*
_{
awc
} with *R*
_{
w
} = 11,5 cm. The *C*
_{
awc
} was simulated using the spectrums of 80 kVp. The σ corresponds with a Reconstruction Diameter *F*
_{
6
} = 30 cm and kernel H30s. A minimum *C*
_{
awc
} is feasible with a resulting average pixel noise of 20 HU (*F*
_{
1
} = 50 mAs and *F*
_{
3
} = 19,2 mm).

Figure 2.

(a) Surfaces of *C*
_{
pmma,c
} associated with *F*
_{
1
} , *F*
_{
3
} and both diameters of standard PMMA phantoms and (b) the average pixel noise associated to *C*
_{
pmma,c
} (represented by *C*
_{
awc
} = *C*
_{
pmmac
} , which is associated with *R*
_{
w
} ) and the Slice Thickness F7.

### Conclusions

The spectrums matched with *C*
_{
a,100
} and *C*
_{
pmma,x
} allow to know quantitatively the contributions of primary and
scattered radiation, and to estimate water equivalent radius adaptive to
size specific quantities. This provides a basis for further modeling of
dosimetric quantities and departure spectrums for in silico simulations
when manufacturer data are not available. Knowledge of noise
association with *C*
_{
pmma,c
} provides a straightforward tool for quantitative optimization,
considering a systemic approach, including a patient - technology -
observer system.