About 80 million CT exams are performed annually in the United States  and CT is the largest source of medical radiation exposure. It contributes to half of the total exposure from medical applications in the United States   and requires accurate dose quantification for both pediatric and adult patients.
The current method of CT dosimetry is based on the computed tomography dose index concept (CTDI), which represents a single axial rotation of the X-ray tube exposure in a CTDI phantom. It is measured with a 100-mm long pencil ionization chamber (CTDI100) placed in a cylindrical PMMA phantom repre- senting the head and body, respectively. Modern CT scanners with helical scanning modes, dose modulation, array detectors and multiple slice planes or cone-beam irradiation geometries make CTDI unsuitable   . The CTDI method is based on two major limitations, firstly the pencil ionization chamber, which is 100-mm-long and used to collect the dose is not sufficiently long enough to measure the tails of the scattered dose distribution  , secondly the CTDI phantoms are 14-cm-long, much shorter than the average adult torso, and cannot replicate the scattered radiation that would occur in a typical adult  .
American association of physics in medicine task group report No. 111 (AAPM TG111)  described a new measurement method that would take into account the scatter of modern CT scanners. They recommend using a small volume ion chamber, and a phantom length that allows for dose equilibrium at the location of the chamber  . As this type of phantom is not commercially available we aimed to construct and characterize a phantom based on the AAPM TG 111 report and measure the accumulated dose and equilibrium dose using a farmer chamber. Our second objective was to compare the dose estimation of the current CTDI standard and independently verify with TLD’s our dose measurements. It’s our hypothesis that the D(eq) method correctly estimates the true patient dose
2. Materials and Methods
2.1.1. Dose Equilibrium Phantom
An in-house water based phantom was developed based on the work of Dixon et al.,   referred to from this point as the dose equilibrium D(eq) phantom. D(eq) phantom was designed and constructed in NUI Galway Figure 1. It is 32-cm in diameter and 50 cm in length. The D(eq) phantom is constructed with a center hole and four peripheral holes. The holes are filled with blanks when not
Figure 1. D(eq) phantom with ion chamber fitted in the center.
in use. It is designed to be transported empty, and once placed on the table, it can be quickly filled or emptied with a small pump operating from a room sink as a reservoir. This phantom size was chosen in order to represent the attenuation and absorption characteristics of the average size adult body. The material composition of the phantom was based on IAEA TRS 277  .
2.1.2. Perspex Phantom
The CTDI phantom was a commercial parties from West Physics company. it consisted of two PMMA cylinders: one cylinder represents the head (160 mm diameter) and the other represents the body (320 mm diameter). The length of each cylinder is 140 mm. Each cylinder contains holes large enough to accept a pencil chamber and are filled with Perspex blanks when not in use.
2.1.3. Computed Tomography Scan, Ionization Chambers and TLDs
A Philips, AcQsim CT was used for these measurements. Dose measurements were taken using Farmer chamber (PTW type 30013) Figure 2 and pencil chamber (Unfors xitm). Both are ionization-based chambers. The Farmer chamber collection volume is 0.6 cm3. It was calibrated by the National Standards of the German National Laboratory. A PC electrometer from Sun Nuclear was used for the Farmer chamber, configured with a cable long enough to allow the electrometer to operate outside the scatter-radiation field, in order to avoid inducing extraneous currents in the electrometer. The PC electrometer provides a bias voltage of ±300 Volts, and it has sensitivity and a leakage current consistent with the farmer ionization chamber volume and dose rate.
The pencil chamber is 10 cm long and was calibrated by Unfors RaySafe. Dose verification was performed independently using thermoluminescent dosimeters (TLDs 100H) Figure 3 which were independently check for accuracy.
2.2.1. Beam Attenuation in the (D(eq)) Phantom and CTDI Phantom
The dose output from one single slice in the middle of the D(eq) phantom and Perspex phantom by using the pencil chamber was used to validate the dose attenuation from D(eq) phantom. For this work, the sequences were: axial scanning mode, kV = 130 kVp, 100 mA, N = 1 mm (number of slice) and T = 5
Figure 2. PTW pharmer champers.
Figure 3. TLD 100H chips.
mm (tomographic section nominal width).
2.2.2. Using Farmer Ionization Chamber
1) Accumulated dose
Scanning a D(eq) phantom moving along the z-axis through a rotating x-ray produces an accumulated dose that can be envisaged as a dose amassed by superpositioning stationary, longitudinally displaced single-scan dose profiles.
With the small ion chamber method, the accumulated dose is directly measured by integrating the current from an ion chamber located at a fixed point in the phantom at the mid-point of the scanned length Figure 4  , while the D(eq) phantom central axis was aligned with the CT rotation axis. The farmer chamber was placed in the phantom in order to center the charge collection volume. The electrometer, which was placed outside the scan room, was connected to the farmer chamber using a cable that reduced the extra chamber current. The charge collected in the ion chamber (nC) was converted to accumulated dose D(0) as follows:
where (nC) is, the total charge collected by the ionization chamber during scanning over the length L, (mGy/nC) is the ionization chamber calibration factor supplied by national standards of the German national laboratory,
and is the ratio of the mass energy ab-
sorption coefficient for water to air. This ratio will vary somewhat with kVp, with the phantom, between the central and peripheral axes and even as the ionization chamber moves along the z-axis. However, the variation is less than 3%   . By following the IAEA TRS-277  , the energy absorption coefficient ratio water to air was 1.036.
The accumulated dose in center and peripheral locations was measured for frequently clinically used protocols  . The parameters of each protocol are detailed in Table 1. Protocol 1 is used for head and protocol 2 for chest. The third one is used for the abdomen.
Figure 4. Farmer chamber position (center and peripheral).
Table 1. Details for the sequence of the protocols used. (n = slice number, T = slice width, b = table increment in a sequence of axial scanning or continuous table advance per rotation during helical scanning).
2) Equilibrium dose
The equilibrium dose is based on an upper limiting value that is derived from the relationship of the scanning length and cumulative dose. When the scanning length (L) increases, the cumulative dose at z = 0 increases along with accumulating contributions from the (scatter tails) outlying scan sections, toward an upper limiting value in which the source of scatter radiation only makes negligibly small additional contributions. The equilibrium dose D(eq) is given by:
  (2)
The h(L) is approach to equilibrium function, where h(L) = 1 when L becomes large enough to yield scatter equilibrium at z _ 0. h(L) has an approximate form as a constant plus an exponentially dependent term leading to saturation  . The equilibrium dose was determined for both the centre and peripheral axes for three protocols (Table 1) then the volume average equilibrium dose   was measured by Equation (3) and compared with the CTDI volume.
  (3)
3) Using pencil ionization chamber
Computed tomography dose index concepts are well documented and it is the primary dose measurement in CT scan currently   . Computed tomography dose index (CTDI) represents the average absorbed dose, along the z-axis, from a series of contiguous irradiations. It is measured from one axial CT and is calculated by dividing the integrated absorbed dose by the nominal total beam collimation   .
  (4)
where the radiation dose profile along the z-axis, N the number of tomographic sections imaged in a single axial scan and T the number of data channels.
The CTDI was proposed and established in the USA by the Food and Drug Administration (FDA)   . It is measured by using 100 mm long ionization chamber and determined by
   (5)
The CTDI100 was determined for central and peripheral axes for three protocols using the Perspex phantom. To make a comparison between the CTDI approach and dose equilibrium method, we utilized the approach of dose equilibrium, by taking the dose from the pencil chamber for one slice and multiplied by 100 then dividing by number of slices and the thickness (NT) of the beam (using Equation (5)) determining the dose profile over the whole chamber. This allows the assessment of CTDI volume and allows the comparison of it with the volume average equilibrium dose.
2.2.3. Using TLD-100H
Dose measurements were also performed in the D(eq) phantom using thermoluminescent dosimeters (TLD-100H) for the verification of the dose calculation by farmer chamber (dose equilibrium method). TLD-100H chips have a high sensitivity and they are commonly used in diagnostic radiology. However, they have different annealing and reading requirements than other TLDs. TLD-100H chips must not exceed a temperature of 240˚C and the recommended annealing cycle for TLD-100H chips are 240˚C for 10 minutes  .
Twenty chips of TLD-100H were calibrated with a diagnostic X-ray system. The luminescent signals were measured by an automated TLD reader (Model 3500, Harshaw), the calibration factor for the TLDs was determined by using the signal integration of the last two peak  , the calibration factor was 0.00385 mGy/nC. Three of TLDs chips where excluded as they were found to be two standard deviation away from a mean.
Four TLD chips Figure 5 were placed in the center of D(eq) phantom for each protocol, and the average of four readings for each protocol is reported and compared with dose values obtained from the farmer chamber.
3. Results and Discussion
3.1. Beam Attenuation in the D(eq) Phantom and CTDI Phantom
The dose outputs from the D(eq) phantom and the Perspex phantom are 0.34 ± 0.01 mGy and 0.33 ± 0.01 mGy respectively as shown in Table 2. Thus, the dose attenuation in D(eq) phantom is equivalent to the dose attenuation on any standard CTDI phantom.
3.2. The Volume Average Equilibrium Dose
The volume average equilibrium dose is obtained by using Equation (3). The central and peripheral were measured for three protocols to find the volume average equilibrium dose, which listed in Table 3. The volume average equilibrium
Figure 5. TLD chips in the center of D(eq) phantom.
Table 2. Single slice dose output at the center of D(eq) and Perspex phantoms.
Table 3. Volume average equilibrium dose.
dose was 12.3 mGy for all protocols.
3.3. CTDI Volume Measurements and Comparison with the Volume Average Equilibrium Dose
The CTDI volume was measured by a Perspex phantom for all protocols and compared to the volume average equilibrium doses for head, chest and abdomen, resulting in an underestimation of 32%, 35% and 25% respectively across the three protocols. This data is presented in Table 4. Additionally, the measured single slice dose profile at the center of the D(eq) phantom Figure 6 indicated that the scan length of 100 mm was not long enough to measure all the tails of the scattered dose distribution, confirming that the CTDI methodology is no longer adequate to accurately characterise CT dose performance.
3.4. TLD Measurement and Comparison with Equilibrium Dose
The comparison between the TLD in center Figure 5 and dose equilibrium in center is shown in Table 5. The variation between the TLD and equilibrium dose for all protocols was less than 5%; therefore, TLD confirmed the accuracy of the dose equilibrium methodology.
Organ and tissue radiation dose prior to a CT scan is currently estimated in Ireland’s health service using the IMPACT software  and other healthcare system use similar estimates. These estimates are based on detailed system specific Monte Carlo simulations and a mathematical model of human phantoms  .
The organ dose and accumulative dose are based on CT dose indexes (CTDI), which we have shown to underestimate the dose. As can be seen (Table 4), the 10-cm chamber measurement underestimates the actual dose by 25% to 35%.
Table 4. CTDI volume compared with volume average equilibrium dose.
Table 5. TLD compared with equilibrium dose.
Figure 6. Single slice dose profile at the center.
Descamps et al.  , determined the volume equilibrium doses for chest, prostate and metastasis protocols to be 12.3 mGy, 12.3 mGy and 12.5 mGy, respectively. This was compared to the CTDI volumes for the same three protocols, which were 9.1 mGy, 9.3 mGy and 9.3 mGy, respectively. They reported underestimation of 30% to 35% in dose as measured by CTDI. Furthermore, Dixon et al.  , found that the current methodology based on the measurement of the integral of the single slice profile using a 10 cm long ion chamber is underestimate the equilibrium dose and dose line integral by about 20%. Thus the two studies are in good agreement with our findings.
The 100-mm pencil chamber is too short and it underestimates the limiting equilibrium dose for any scan length above 100 mm. As a result, the tissue weighted organ dose obtained from IMPACT software may underestimate the radiation dose absorbed by the organs, increasing patient risk.
Alternately, using an ion chamber shorter than 1 cm, and a phantom long enough to establish dose equilibrium in the center we can provide a more realistic dose estimate. In addition, a measurement of accumulated dose can be determined at any point in the phantom not just at the center of the scan length which is the only location at which the pencil chamber in CTDI can measure accumulative dose to formalize a dose prediction. The dose equilibrium method is more flexible and not significantly more time consuming than the current method that uses a long chamber.
Stuart Harris NUIG for help constructing the phantom, Sinead Cleary and Michael O’Conner Galway University Hospital for organizing access and training on the CT system and Matthew Donoghue for organizing access to a CTDI phantom and pencil ion chamber. The authors would also like to acknowledge the input of Prof Van der Putten who has sadly passed away.