Radiation dose in x-ray computed tomography (CT) has become a topic of high interest due to the increasing numbers of CT examinations performed worldwide [1,2,3,4,5]. Studies underlined the increase over the years in the number of CT examinations resulting in an increase in the dose per capita for the population. For the USA, Brenner et al. [6, 7] reported that the number of CT examinations per year rose from 2.8 million in 1981 to 20 million in 1995 and to 62 million in 2007. In Germany, from 1996 to 2012, the annual effective dose per capita for CT examinations has more than doubled . A retrospective analysis carried out in Italy (Lombardy district) between 2004 and 2014  showed a 39% increase in the number of CT examinations per 1,000 residents.
A CT scan involves a dose larger than the most common radiographic procedures. Depending on the acquisition setup, the dose to the organs included in the scan region was reported to range from 15 mSv for an adult to 30 mSv for a newborn, with an average of 2–3 scans per study . With the increase in the collective dose for medical exposures, there has been an increase in publications focused on radiological risk estimation [10,11,12].
Exposure from a diagnostic CT examination is referred to have a stochastic effect. An epidemiological study of radiation-induced tumour risk for patients undergoing CT procedures first requires an assessment of the dose delivered to the organs and tissues exposed. The organ dose is defined as the dose received by the specific organ per unit of mass. It mainly depends on patient’s anatomy, scan region, and scanner’s output. Its estimate is the basis for risk analysis. However, the dose to the organs is not an immediate information easy to be obtained. Samei et al.  defined its determination as a Holy Grail . In the 1990s, the European Commission (Council Recommendation 1999/519/EC) encouraged the research of new methods to estimate the patient dose in CT. The general approach was the use of a Monte Carlo algorithm associated with an anthropomorphic phantom [14,15,16].
In this context, the first software applications for organ dose calculation were born. In general, all applications are based on the same principle: they use a set of organ doses, pre-calculated on single sections, typically 1-cm scans, which are combined to obtain the entire scan region and adjusted according to the exposure parameters in use [15, 17].
To date, several software have been introduced to calculate the organ dose in CT. Since the 1990s, there has been an evolution of calculation methods and graphic presentations, thus allowing for an easier use. When choosing a software application for organ dose CT calculation, we should consider phantoms, algorithms, reference device and validation (if available). Phantoms include the most elementary mathematical types up to hybrid voxel computational ones, which allow more reliable estimates . The calculation algorithm, combined with the scanner modelling, allows to create a set of dose coefficients used to calculate the organ dose. Some software use a limited set of these coefficients and a number of correction factors to adapt the result to the reference conditions variation, such as tube voltage or phantom . By reference device we mean, the scanner model used to simulate the photons histories in the Monte Carlo code. Generally, these software applications present a list of devices from which the user can select the one of interest. Obviously, older software does not include new generation scanners.
Among the software applications we analysed, the CT-Expo (G. Stamm, Hannover and H.D. Nagel, Buchholz, Germany) is the only one that uses a family of mathematical phantoms (Adam, Eva, Child, Baby), for which the body surface and organs are expressed by equations. It is also able to simulate the modulation of the beam in the CT scan and to choose between axial and spiral mode . It is an application usable in the Excel® (Microsoft Corporation, Redmond, United States) environment, based on the computational method developed by Stamm and Nagel  for the analysis of data collected in the survey conducted in Germany in 1999 and 2002.
The National Cancer Institute CT (NCICT) dosimetry system (National Cancer Institute, Bethesda, USA) [22,23,24] uses hybrid voxel computational phantoms (University of Florida family). In general, voxel phantoms are defined starting from the segmentation of CT images of patients with dimension close to the reference. Non-uniform rational basis-splines surfaces are introduced in hybrid phantoms to maintain the flexibility of stylised phantoms for anatomy modifications. In this way, it is possible to adapt the stylised phantom to the reference dimension indicated by the International Commission on Radiological Protection (ICRP) for both genders [25, 26]. In addition to the adult phantoms, the software also allows to select paediatric phantoms for newborn, 1, 5, 10 or 15 years of age.
The NCICTX software (National Cancer Institute, Bethesda, USA) implements the same NCICT hybrid voxel computational phantoms family but enhanced to better adapt to the size of the patient under study, following the National Health and Nutrition Examination Survey (NHANES) IV database . The NCICTX phantom library contains 100 adult males, 93 adult females, 85 males and 73 females of paediatric age, with different mass and height combinations , defined starting from the NCICT phantom. The NEXO[DOSE]® software (Bracco Imaging, Milan, Italy) integrates NCICTX directly in the application, without external Internet connection.
Virtual Dose, an application funded by the National Institute of Biomedical Imaging and Bioengineering (NIBIB, USA; https://www.nibib.nih.gov/), presents a ‘software as a service’ (SaaS) architecture, for which the application can be accessed remotely through a web-based interface, without the need to install the software locally [29, 30]. NEXO[DOSE]® integrates the Virtual Dose functionality through a RESTful application program interface. Its library includes a set of voxel phantoms representing men, women and children of different ages (newborn, 5, 10, and 15 years of age) [31, 32]. It also represents pregnant women, considering the three gestation trimesters, and obese patients with different mass index [33, 34].
The aim of this study was to compare these four commercial software applications (CT-Expo and NCICT as stand-alone software applications, NCICTX and Virtual Dose, integrated within the NEXO[DOSE]® radiation dose monitoring system) in terms of dosimetric data variability, both as organ dose and as effective dose, using different calculation methods, including the simulation of different exposure CT parameters.