Here is a simple calculator to compute the Effective Dose (mSv) from the Dose Length Product (mGy cm) for a CT exam of a single organ. In this article we review how dose measurements are made and how the Effective Dose is related to the Absorbed dose, and the approximation that is used in CT to offer a simplified method to calculate the Effective Dose.

In this calculator we provide a quick way to convert from the Dose Length Product (DLP) ( mGy*cm) to the Effective Dose (mSv). This conversion depends upon the body part and the age of the patient. As we will describe below this is an approximation of the effective dose but it is reasonably accurate (typically within 10-15%) and it is easy to compute.

The CT scanner will typically output the CTDI (mGy) and the DLP (mGy*cm). This calculator takes the DLP as input and calculates the effective dose as described below. For those interested we will review the dose methodology below for CT.

## Absorbed Dose (mGy)

The first step in calculating the effective dose is to measure the absorbed dose. Absorbed dose is calculated using a ‘phantom’ which roughly mimics a patient (the term phantom just means an object that we put in the scanner to mimic a patient in some way).

Typically, a plastic cylinder is used as it has similar x-ray absorption properties to tissue in the body. We want to measure the energy deposited in the phantom. The absorbed radiation dose is defined as the energy absorbed per unit mass. The units that we have typically use are the SI units of Gray (Gy) which is defined as Joule/kilogram (J/kg). We are typically dealing with doses that are a fraction of a gray in radiology, so we often talk about a milli-gray which is 1/1000^{th} of a gray.

## Computed Tomography Dose Index (CTDI)

CTDI is measured with a phantom where we have again a plastic cylinder as it is a tissue mimicking material. An ion chamber is inserted into this plastic cylinder. The ionization of the air inside the chamber is measured and that signal is proportional to the radiation dose deposited in that chamber (see our post on Radiation Dose for more info). That measurement is done for four outer (peripheral locations) and then one central location within the phantom.

There are many different methodologies or definitions of the CTDI that have come about over the years as scanners have increased in complexity (first adding helical scanning and then adding wide coverage scanning). These include CTDI, CTDI_{FDA} , CTDI_{100} , and CTDI_{vol }. As a radiologic technologist you do not need to be really concerned with which CTDI definition is used as long. The vendors work to match standards that the medical physicists define for these definitions.

The different methodologies are necessary because the scanners have wider and wider columniations. This is why the methodology had to be updated for calculating the CTDI. But in general, the CTDI is the absorbed dose for the system, for that phantom size (see our post on Constant Radiation Dose in CT for more info on why CTDI is a surrogate but is not a measure of the actual patient dose).

## Relation of Radiation Measures

To get from absorbed dose to an equivalent dose, in the case of x-ray radiology such as CT scans, we multiply by 1. Thus, we don’t really have to do anything to convert to equivalent dose. In other scenarios if a different radiation source was being used there may be a different weighting factor.

Then to get from an equivalent dose to an effective dose, you need to take into account which organs are receiving the radiation dose as there are different weights depending upon the biological impact on the different tissue types.

## Effective Dose (mSv)

To convert from equivalent dose to effective dose we multiply the dose to each organ by a weighting factor associated with that organ. These weighting factors are defined by the ICRP and account for the different radiation sensitivities of different tissue types.

In general, the list of weightings for the different organs shows us that for instance comparing the gonads with the brain, you would rather receive that given radiation dose to the brain because it’s less radio sensitive than the gonads for instance as it has a lower weighting (for more info on why different tissue types have varying sensitivities see our post on Radiation Biology).

The effective dose, again we take the equivalent dose and we weight all the different organs based on the radiation dose each organ received. If we want to do this properly, we have to either measurements in phantoms, which are anthropomorphic (ie. like the human body that we are scanning). Or you have to do Monte Carlo simulations where you simulate the x-rays passing through the anatomy. Or some combination of phantom measurements and computer simulations of the radiation dose. or some combination of those two.

All this gives you Effective Dose (mSv) numbers where we can figure out how much of the brain, how much of the gonads, and how much of the other organs are receiving radiation dose in a very specific manner. However, these methods are also a very complex as we need to model each patient.

The effective dose, again we take the equivalent dose and we weight all the different organs based on the radiation dose each organ received. If we want to do this properly, we have to either measurements in phantoms, which are anthropomorphic (ie. like the human body that we are scanning). Or you have to do Monte Carlo simulations where you simulate the x-rays passing through the anatomy. Or some combination of phantom measurements and computer simulations of the radiation dose. or some combination of those two.

All this gives you Effective Dose (mSv) numbers where we can figure out how much of the brain, how much of the gonads, and how much of the other organs are receiving radiation dose in a very specific manner. However, these methods are also a very complex as we need to model each patient.

## Dose Length Product (mGy cm)

Luckily for us there is a simplified method to arrive at approximate estimates of the Effective Dose (mSv). We first need to define the Dose Length Product as this will be used in the approximate Effective Dose (mSv) calculations.

As discussed above CTDI is a measure of the absorbed radiation dose, the absorbed dose for a given size phantom.

Then we need another method to take into account how long the scan was, namely what is the scan length along the SI direction (ie. the direction parallel to the patient table).

Since the CTDI is normalized to some given length across this direction we need to multiply by the scan length to calculate the dose length product (DLP).

This is a nice name as Dose Length Product (DLP) directly describes what the quantity is as it is the product or multiplication of those two terms (DLP (mGy*cm) = CTDI (mGy) * Scan Length (cm).

We can think about two scans which have the same CTDI but which cover different ranges of the patient anatomy. It is clear that we would like to treat these scans differently when considering the radiation dose to the patient.

This is why we need to use the DLP and we can keep track of the scan range dependence by just multiplying by the scan length, as mentioned above. Now that we have the DLP we need a method to calculate and approximate Effective Dose (mSv) from the DLP.

## Approximate Radiation Measures CT

Now, that we have defined both the CTDI and the DLP we can present the approximate method that can be used to estimate the Effective Dose for CT scans.

You can see that this figure looks similar to the one presented above for Radiation Dose in x-ray Radiology. However, in this figure we present the approximate method.

The input for this approximate method is the CTDI measured in a representative phantom, 16cm for adult heads and 32 cm for adult bodies.

Along with the CTDI we need to know the scan length in order to compute the DLP (DLP (mGy*cm) = CTDI (mGy) * Scan Length (cm)). In the dose report the CT scanners will typically output both the CTDI and the DLP.

The final step to compute the approximate Effective dose is to multiply the DLP by a conversion factor that we call ‘k’ here. That conversion factor is dependent on the body part(s) being scanned, and the patient age.

If you are scanning the head the conversion factor will be smaller than if you are scanning the abdomen/pelvis as the tissue is less radiosensitive in the head.

There is also an age dependence as radiation impacts are higher for younger patients (especially young children).

As included in the AAPM task group report on Radiation Dose Reporting, the values for the conversion factor that are used in the calculator above are:

Region of Body | 0 year old | 1 year old | 5 year old | 10 year old | Adult |

Head and Neck | 0.013 | 0.0085 | 0.0057 | 0.0042 | 0.0031 |

Head | 0.011 | 0.0067 | 0.0040 | 0.0032 | 0.0021 |

Neck | 0.017 | 0.012 | 0.011 | 0.0079 | 0.0059 |

Chest | 0.039 | 0.026 | 0.018 | 0.013 | 0.014 |

Abdomen and Pelvis | 0.049 | 0.030 | 0.020 | 0.015 | 0.015 |

Trunk | 0.044 | 0.028 | 0.019 | 0.014 | 0.015 |

Note that this is much simpler than running a computer program: where you take the CT volume as input, segment out all the organs, calculate the dose delivered to all the organs through sophisticated simulations and sum the contributions to the effective dose based on the weights for each organ.

This approximation that we are using here It is much simpler as all we’re doing is multiplying two numbers together.

This is actually surprisingly effective and matches those more sophisticated methods within 10-15%.

We have presented the simplified framework for calculating the Effective Dose for CT scans via a conversion from DLP to mSv. Next, we will present a couple of representative examples of use of the calculator.

## Calculation Examples

At the top of the page we have the calculator where we enter the DLP, patient age and region of the body in order to calculate the effective dose (i.e. DLP to Effective Dose).

We will give a couple simple examples here of using the calculator to compute the effective dose. The CT scanner will typically output both the CTDI (mGy) and the DLP(mGy*cm).

For instance for the head there may be a CTDI of 50 mGy and then just for round numbers, imagine we’re scanning just the head and the length is 20 cm. So, the DLP for that exam will be 50mGy*20cm=1000mGy*cm. If we are scanning an adult head with that DLP the effective dose is about 2 mSv. If however we switch to a newborn patient of age 0 the effective dose would be about 6 milli-sieverts, because of the age of the patient.

If we come back to the standard head scan on an adult we can put the 2mSv into context. For reference, the background radiation dose of the United States is about 3 milli-sieverts. So, this standard head exam has a radiation dose of roughly 2/3 of the background radiation dose. For more information on representative doses in terms of background radiation please see our post on background radiation.

The next example we will consider is the CT scan of a chest. Imagine we have a chest and we’re doing that scan with technical parameters that lead to a CTDI of 10 mGy. For this exam imagine we have a coverage of 50cm. Thus, we’re looking at 50mGy*10cm=500mGy*cm for our DLP.

If we input 500mGy*cm for the DLP and assume that we are scanning an adult chest and then we will have an effective dose of about 7 mSv. Again, this is a little bit higher than in the head because of the biological weighting factors associated with different body parts.

If we compare that to the effective dose that we’re talking about for background radiation, this dose is equivalent to a little more than 2 years of background radiation.

These are just a couple of examples of how to use this simple calculator. Please go through on your own so that you can become more familiar with the relationship between the DLP in CT (the body region and the patient age) and the Effective Dose. We hope that you find this to be a useful tool.