An interactive calculator for changing multiple technical parameters (kVp, SID, s, Bucky Factor) in and observing the effect on the mA needed to keep the exposure on the image receptor constant. Great for studying for your ARRT boards or brushing up to sharpening your technical parameter skills for Radiography exams.
X-Ray Exposure Calculator
Overview of Technical Parameters
As a technologist you are often faced with the situation where you need to make a change to a protocol but want to keep the exposure on the detector the same. In this scenario it is really important to understand the technical parameters and their influence the exposure, so that when changing parameters you do not end up under-exposing or over-exposing the image receptor (film, CR or DR).
The technical parameters which control the exposure measured on the detector and also the radiation dose delivered to the patient are summarized in the table below and include (mA, kVp, s, SID and Bucky Factor). In the following sections we will describe each in a bit more detail and link to other resources where these concepts were introduced and covered more completely.
As a technologist you need to commit these dependencies to memory so that you can have an intuitive or gut feeling about the changes in technical parameters and this will help you to provide the best acquisitions for your patients. At the end of the this post we put these into one big equation, but you can see from this table that there are really just FIVE SIMPLE RELATIONSHIPS that you need to know to master your technical parameters.
|Technical Parameter||Units||Exposure Dependence|
|Tube Current||mA (milliAmperes)||mA|
|Tube Potential||kVp (kilovolt potential)||kVp5|
|Exposure Time||s (seconds)||s|
|Source to Image Distance (SID)||cm (centimeters)||1 / SID2|
|Bucky Factor (Scatter Grid Factor)||unitless||1 / Bucky|
mA (tube current)
The tube current in the x-ray exam is the parameter that is most frequently changed and you should consider this as your first go-to adjustment in order to change the x-ray exposure without impacting the quality of the exam in other ways (i.e. the contrast and motion artifacts are not affected).
Increasing the tube current is actually just providing more electrons that with smash into the x-ray target and thus produce more x-ray photons. For more details on the x-ray tube and influence of mA check out our articles on x-ray generation and beam quality.
kVp (tube current)
The kVp is the most important technical parameter as it has a very strong dependence on the x-ray exposure (kVp5). This strong dependence on the kVp for the exposure at the image receptor is because of the higher flux and stronger penetration of higher kVp imaging. Additionally, the kVp also changes the inherent contrast in the x-ray images.
Since it does impact the x-ray contrast changes to the kVp of an exam need to be considered more carefully than changing the mA, but there are definitely times when it is needed.
As the kVp is increased the x-ray beam becomes more penetrating. This is a good thing for passing through large anatomy. On the other hand as the kVp is increased the relative contrast between tissues in the body is reduced (x-ray contrast). As the kVp is increased there is also a higher contribution of Compton scatter events. Therefore, the general rule is use the lowest kVp which will still provide a good exposure on the image receptor.
This is one reason why mammography exams are performed at a low kVp and a large abdominal x-ray is performed at a higher kVp.
Since x-ray exposure goes approximately as kVp5 and we generally don’t think in powers of 5 a well known approximation is typically used called the 15% rule of kVp of radiography. This rule comes from the fact that 1.155 ~2.0. Therefore, for each increase of 15% in kVp the exposure will double. Thus, if the kVp is increased by 15% then the mA must be decreased by a factor of 2 in order to maintain constant exposure on the image receptor.
Changing the kVp of an acquisition changes the tube potential so that as the electrons collide with the x-ray target they will have more energy and thus produce higher energy x-ray photons (x-ray generation).
The time of the exposure is a relatively easy concept to understand. As the time of the exposure is increased by a factor of 2, the number of x-ray photons coming out of the x-ray tube will also be increased by a factor of 2. This is why the exposure dependence on (s) is also linear as it is with mA.
It is also intuitive that as the exposure length is increased there is a higher likelihood of motion within the x-ray image. Depending on the exam type this may or may not be a major concern. For instance during an x-ray of an extremity of a well informed patient the anatomy of interest can remain relatively still, while in a chest x-ray the lung anatomy near the heart will be moving regularly along with the heart muscle.
SID (Source to Image Distance)
The Source to Image Distance (SID) affects the exposure at the image receptor since the x-ray beam is divergent (i.e. spreading out as it gets further from the x-ray tube).
Since the x-rays are spreading out the exposure depends on the SID as 1/SID2 . In our post on the basic x-ray properties we demonstrate how the divergent beam leads to the 1/R2 dependence and in this case the distance R from the source to the image receptor is also referred to as SID.
Since this is an inverse relationship if we move the image receptor further from the x-ray tube another technical parameter must be updated to maintain the exposure. For instance, if the SID is increase by a factor of 2 from 50cm to 100cm the mA will need to be increased by (100/50)2=22=4.
Bucky Factor (Scatter Grid Factor)
Finally, the Bucky factor is a unitless quantity which is the ratio of the x-ray exposure reaching the grid to the x-ray exposure reaching the image receptor. If no grid is used this definition will lead to a Bucky factor of 1.0.
The Bucky factor for grids is dependent upon the grid ratio (grid height: grid spacing) and the kVp. It typically ranges from 2.0 – 6.0 for diagnostic x-ray grids. More details on the Bucky Factor in the X-ray Scatter post.
The x-ray exposure on the image receptor scales as 1/(Bucky Factor). Therefore, if you have a higher Bucky Factor for the new grid you will have to increase the exposure by changing another technical parameter such as increasing the mA.
For instance if the initial protocol did not use any grid (Bucky=1) and the new protocol uses a grid with a (Bucky=2.0). Then the mA will need to be increased by 2.0 in order to keep the exposure constant on the imaging receptor.
Golden Equation (All Technical Factors)
Now that we have all pieces we can put these 5 simple relationships together to make what we call the golden equation. You can give it your own cool name too. We just call it the golden equation since it has all of the factors that you need to consider so that as you change one factor you can compensate to keep your exposure constant.
Also this is just a calculator for demonstration purposes so it does not have limits on the mA. I know you wish your actual system was like that too. Since our physical systems often have limits on the mA you may need to compensate in other ways such as increasing the length of the acquisition. That can still be accomplished with this framework and with the calculator above.
We start by writing down each of the terms that are proportional to the exposure from the sections above so that we get one equation containing mA, kVp, s, SID and Bucky Factor.
Now that we have the exposure relationship with our technical parameters we consider your real world problem where you have an original protocol and one or more of the technical parameters needs to change. In this case the new exposure will be denoted as Exposurenew and we want it equal to the original Exposure.
Combining the two equations above we see that we can write the new exposure out in terms of all of the technical parameters, and the original exposure as well.
Then we can solve for the mAnew, by dividing by the terms in the numerator on the left hand side, and multiplying by the terms in the denominator on the right hand side. Now we have what we call the golden equation that is implemented in the calculator above so that we can compensate for any changes to technical parameters without over or under exposing your image receptor.
There is no magic here, just one equation to study up on. Once you start having dreams (not nightmares) about this golden equation then you know that you have probably studied it enough.
Obviously, if one of the parameters is not changed from the original to the new set of parameters then that term will cancel out as we will just be multiplying by 1.
So for instance if you are only changing one parameter you can refer to this table to determine how to change the mA in order to compensate for your parameter change. This table is just another way of summarizing the golden equation.
|Technical Parameter||Units||Multiplier to mA|
|Tube Potential||kVp (kilovolt potential)||(kVp/kVpnew)5|
|Exposure Time||s (seconds)||(s/snew)|
|Source to Image Distance (SID)||cm (centimeters)||(SIDnew/ SID)2|
|Bucky Factor (Scatter Grid Factor)||unitless||Buckynew / Bucky|
Now that you have read all the way through on the details of the golden equation make sure to write it down yourself with a pencil/pen and paper and try several examples so that you can get familiar with it.