# Solving crime with blood and maths

US researchers have developed a new way to interpret spattered bloodstains, potentially enabling police to reconstruct a crime more accurately.

But the new approach doesn’t involve ultraviolet lights, microscopes, test tubes or any of the other techniques favoured by police television dramas. Instead, these researchers use maths.

The team from the University of Illinois at Chicago and Iowa State University have used both mathematical modelling and physical experimentation to produce an approach that, they say, overcomes weaknesses in current crime scene forensics.

The goal of crime scene reconstruction is to work out what happened during a crime. This can be accomplished through a set of techniques called bloodstain pattern analysis (BPA).

BPA experts analyse a blood spatter pattern to find out what weapon or action caused the injury, when the incident occurred, and where the perpetrator and victim were at the time.

A common crime scene reconstruction technique called the “method of strings” is often used when blood is splattered across an area. A straight string is drawn back from each bloodstain as far as possible, and where the strings converge is assumed to be the point of origin of the blood spatter pattern, and thus the victim.

However, this approach has several weaknesses, the research team writes in the journal Physics of Fluids.

“The inherent assumption that droplet trajectories are straight ignores such physical phenomena as gravity, air drag, and droplet-droplet interactions. Overall, these limitations make the method of strings inaccurate.”

In fact, current techniques sometimes cannot even tell whether splattered blood is from a shooting or a beating.

The researchers realised that gaining a better physical understanding of the fluid dynamics at play during gunshot spatters could enhance crime scene investigations.

So they started by shooting two types of bullets (a 7.62×39 millimetre bullet and .45 auto bullet) into a foam core board containing pockets of human blood, and capturing the blood patterns on butchers’ paper, which were then analysed.

This information was fed into complex mathematical modelling drawing on percolation theory, which studies the filtration of liquid through a porous medium.

The modelling also takes account of the viscoelastic nature of blood – which means it does not disperse as simply as, say, water – and the fact that a bullet entering a body may cause blood to spatter both forwards and backwards.

As a result, the team has come up with a general model for predicting how blood will disperse as a result of gunshot.

Lead author Alexander Yarin says this tool may help forensic examiners to “crack tough questions” about a crime scene.

“Our results revealed that bullet shape and velocity determine the blood spatter patterns, because they dictate the velocity field in the blood body,” he says.

“This will allow a more accurate determination of the origins of blood spatter, as well as potentially facilitate investigators’ conclusions about the weapon used for cases in which a bullet is not found.”