The subtraction process

Step 1: Mask acquisition

A mask image is obtained before contrast administration.
This image represents the unenhanced anatomy (soft tissue, bone, background).
It is typically acquired under the same exposure conditions as the live images to ensure comparable signal levels.

Step 2: Contrast-enhanced sequence

After injection of iodinated contrast, a rapid sequence of live images is acquired at frame rates of 3–15 frames per second, capturing the contrast bolus as it passes through the vascular bed.

Step 3 option 1: Linear subtraction

The mask image is subtracted from each live image:

I_sub(x,y) = I_live(x,y) − I_mask(x,y)

This removes all structures that remain constant between frames (bones, soft tissue), leaving only pixels whose attenuation has changed i.e. contrast-filled vessels.

Step 3 option 2: Logarithmic conversion and subtraction

Because X-ray attenuation follows an exponential relationship with tissue thickness and attenuation coefficient, subtraction is more accurate in the logarithmic domain:

I_sub = log⁡(I_mask) − log⁡(I_live)

This logarithmic subtraction linearises the exponential attenuation curve, ensuring that equal differences in iodine concentration produce proportional signal changes.
The output is typically displayed in inverted greyscale, with contrast-filled vessels appearing bright on a dark background.

Subtraction method	Basis	Advantages	Limitations
Linear subtraction	Direct pixel difference	Simple, fast	Inaccurate if exposure or beam quality changes
Logarithmic subtraction	Derived from Beer–Lambert law	True linearity with iodine concentration	Requires stable exposure and detector calibration

*The astute amongst you may notice that with the logarithmic conversion the live is subtracted from the mask. This is because the logarithmic conversion is subtracting attenuation values whereas straightforward subtraction (described in step 3) is subtracting brightness values. It is a very minor point, that doesn’t really have any influence of questions in the exam. But I’m putting this here as a fyi.

Image registration and motion artefacts

Misregistration

Any movement between mask and live images causes misalignment, resulting in incomplete subtraction and residual “ghost” structures.

Type of motion	Source	Mitigation
Patient movement	Voluntary motion, breathing, cardiac pulsation	Immobilisation, breath-hold instructions
Table movement	Mechanical instability	Stabilised support, consistent positioning
Contrast-induced vessel motion	Flow dynamics	Fast exposure, pulse synchronisation

Even submillimetre misregistration can introduce visible artefacts in subtracted images.

Correction techniques

Several post-processing techniques are used to compensate for small errors in alignment and improve image quality.

Technique	Purpose	Method
Pixel shift	Corrects small translational misalignments	The mask image is digitally shifted by integer or fractional pixels to match the live frame.
Remasking	Replaces the original mask with a new one acquired later in the sequence	Used when the initial mask is contaminated by early contrast or motion.
Recursive temporal filtering	Combines current and previous subtracted frames to smooth noise while preserving motion	Weighted averaging algorithm applied to successive frames.

These corrections are performed automatically in modern DSA systems and can be manually fine-tuned by the operator.

Noise propagation in subtraction

Noise from both the mask and live images contributes to the noise in the subtracted image:

σ²_sub = σ²_mask + σ²_live

Since these are uncorrelated, subtraction increases total noise relative to the original frames.
As a result, adequate photon fluence (dose per frame) and temporal filtering are essential to maintain sufficient signal-to-noise ratio (SNR).

Parameter	Effect on SNR
↑ Dose per frame	↑ SNR but ↑ patient dose
↑ Frame averaging	↓ Noise but ↓ temporal resolution
↑ Detector DQE	↑ SNR efficiency

Key takeaways and exam tips:

• DSA isolates vascular structures by subtracting a pre-contrast mask from post-contrast images.
• Logarithmic subtraction compensates for the exponential attenuation relationship of X-rays.
• Detector linearity and image registration are essential for artefact-free subtraction.
• Noise doubles through subtraction; compensated via dose, filtering, or frame averaging.
• Pixel shift and remasking correct for motion and misregistration artefacts.
• Common exam question: “Describe the principles of digital subtraction angiography and explain how logarithmic subtraction improves contrast accuracy.”

Up next

Next, we will move on to System Design and Acquisition Modes, covering how modern angiography systems are engineered for high-speed image acquisition, pulse control, and synchronised contrast delivery which are all essential for high-quality DSA imaging.