Adventures of a Physicist:
Computational and Laboratory Investigations of a Model
of Blood Droplet Flight for Forensic Applications
Raquel Murray
UOIT
August 23, 2012
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 1 / 35
Introduction
At a crime scene, the reconstruction of bloodletting events can be a keyplayer in solving crimes.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 2 / 35
Methods
The most common method for reconstructing bloodletting events is theString Method.
Can be time consuming
Neglects gravity and drag
Cannot accommodate downwardmoving drops
Figure: Using the String Method to reconstruct a bloodletting event [2]
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 3 / 35
Methods Software Packages
Programs like HEMOSPATTM[6, 7] and BACKTRACKTM[1, 2, 3] also usestraight line geometric reconstructions for bloodletting events.
Use virtual strings Do not account for the forceof gravity or the e↵ects ofdrag
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 4 / 35
Methods BACKTRACK
Figure: Top view from BACKTRACK related to downward moving drops. Theintersections correspond to the blood source location in the plane of the floor [2]
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 5 / 35
Methods BACKTRACK
Figure: Side view from BACKTRACK related to downward moving drops. Threevirtual strings were added from upward moving drops. [2]
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 6 / 35
Methods HEMOSPAT
Figure: HemoSpat Software interface [5]
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 7 / 35
The Problem
What about laws of physics?!
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 8 / 35
Early Laboratory Experiment
Figure: A single camera experiment. The high-speed camera is orientedperpendicular to the path of the projectile to capture the motion of the dropletsin a vertical plane.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 9 / 35
Early Laboratory Experiment
Figure: Still shot from single high-speed camera experiment video.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 10 / 35
Early Laboratory Experiment
Figure: Manual tracking of a single droplet. Here, a single droplet is observed in10 frames from a single camera and the position was marked by the user. TheMegaspeedTM [8] software takes those ten points and applies polynomialinterpolation to reconstruct the path.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 11 / 35
Early Laboratory Experiment
Figure: An approximation of a blood droplet trajectory using the Verlet Algorithm.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 12 / 35
Early Laboratory Experiment
Looks great right?!
This is only a two-dimensional model.
This model is not telling us anything about the parameters involvedwith the flight of blood droplets.
There’s still work to be done...
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 13 / 35
Laboratory Experiment
The laboratory procedure used to generate videos of simulatedbloodletting events is as follows:
1 Prepare mock crime scene and recording equipment.
2 Calibrate the recording equipment.
3 Run the laboratory experiment.
4 Document and verify the experiment.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 14 / 35
Laboratory Experiment Experimental Setup
Figure: Placement of lab jack and paintball gun within the crime scene. A)paintball gun used as a weapon. B) Lab jack on which the ballistics gel is placedin front of the paintball gun. C) Halogen 500W work light.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 15 / 35
Laboratory Experiment Experimental Setup
Figure: The full laboratory setup.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 16 / 35
Camera Calibration
Before shooting the ballistics gel, calibration videos needed to be captured:
1 Capture the moving checkerboard calibration video
2 Capture the moving laser dot calibration video
3 Verify the accuracy of the calibration
4 Capture the riot ball calibration video
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 17 / 35
Camera Calibration
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 18 / 35
Movies
Show stereo videos of pig blood experiment.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 19 / 35
The Droplet Tracker
Figure: Automated tracking of a full experiment using the Droplet Tracker [9].
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 20 / 35
Reconstructed Blood Droplet Paths
!0.1 0 0.1 0.2 0.3 0.4 0.5
!0.2
!0.15
!0.1
!0.05
0
0.05
0.1
x
y
!0.2 !0.15 !0.1 !0.05 0 0.05 0.1 0.15
!0.2
!0.15
!0.1
!0.05
0
0.05
0.1
z
y!0.2 !0.15 !0.1 !0.05 0 0.05 0.1 0.15
!0.1
0
0.1
0.2
0.3
0.4
0.5
zx
Figure: Visualisation of the tracked trajectories from the Droplet Tracker.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 21 / 35
Documenting the Experiment
(a) A digital photograph of a transfer bloodstain in the field of view ofCamera A.
(b) A digital photograph of a transfer bloodstain in the field of view ofCamera B.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 22 / 35
Our Model Purpose
We are looking to achieve the following:
Using a set of initial conditions, produce ODE-based trajectories
Fit those ODE-based trajectories to the experimental pathreconstructions
Estimate the radius, direction, and initial speed of an individual blooddroplet
Investigate the resulting Reynolds number and drag coe�cients fromthese droplets
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 23 / 35
Our Model Dynamic ODE Model
Y
XFg
Fd
directionof motion
Figure: The forces acting upon a single droplet as it flies through the air. Thedrag force (Fd) will oppose the direction of motion and the force of gravity (Fg)acts only in the y direction, pulling the droplet downward.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 24 / 35
Our Model Dynamic ODE Model
We start o↵ our model with Newton’s Second Law of motion:
F = Fd + Fg, (1)
Substituting the drag force (also used by Liu et. al. in [4])
Fd = �1
2⇢airAkuk2u, (2)
and the gravitational force
Fg = �mg. (3)
We obtain
u = �3
8
r
⇢air
⇢dropkuk2u� g. (4)
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 25 / 35
Objective Function
Therefore, the objective function, f , is written as
f(r, u0, ✓0,�0) =kX
t=1
kvt �wtk2 . (5)
The decision parameters are:
radius: r
initial speed: u0
angles: ✓ and �
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 26 / 35
Visual Verification
0 0.05 0.1 0.15 0.2 0.25
!0.16
!0.14
!0.12
!0.1
!0.08
!0.06
!0.04
!0.02
0
x
y
0 0.01 0.02 0.03 0.04 0.050
0.05
0.1
0.15
0.2
0.25
z
x0 0.01 0.02 0.03 0.04 0.05
!0.15
!0.1
!0.05
0
zy
Figure: The red data points are the spatial coordinates of a transfer blood droplettracked by DT. The black line is the ODE-based trajectory with optimisedparameters to reduce the Euclidean norm between the DT trajectory and theODE trajectory.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 27 / 35
Visual Verification
!0.1 0 0.1 0.2 0.3 0.4
!0.5
!0.4
!0.3
!0.2
!0.1
0
0.1
x
y
Figure: An xy view of the DT trajectories (red data points) and each of theirODE-based trajectories (black line). The riot ball is plotted in green, moving inthe positive x direction.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 28 / 35
Conclusion
Collect stereo video data of simulated bloodletting events
Blood droplets are tracked
Successfully fit ODE-based trajectory to experimental pathreconstructions
Retrieves the initial speed, directional angles, and radius
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 29 / 35
Future Work
Backward integrationOscillations or radial distortions of a droplet during its flightHow blood droplets impact di↵erent surfaces
Figure: A digital photograph of the resulting bloodstain pattern formed on acardboard surface from the porcine blood experiment.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 30 / 35
My Future
Research changed the course of my life for the better :)
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 31 / 35
Acknowledgements
THANK YOU
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 32 / 35
References
A. L. Carter.The directional analysis of bloodstain patterns theory andexperimental validation.Canadian Society of Forensic Science, 34(4):173–189, 2001.
M. B. Illes, A. L. Carter, P. L. Laturnus, and A. B. Yamashita.Use of the backtrack computer program for bloodstain patternanalysis of stains from downward-moving drops.Canadian Society of Forensic Science, 38(4):213–218, 2005.
International Association of Bloodstain Pattern Analysts.Ballistic Trajectories of Blood: Computer Applications and Workshop,Reno, Nevada, October-November 1990.
Alex B. Liu, Daniel Mather, and Rolf D. Reitz.Modeling the e↵ects of drop drag and breakup on fuel sprays.Sae technical paper series, University of Wisconsin, Masidon EngineResearch Center, March 1993.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 33 / 35
References
Andy Maloney and Kevin.Hemospat bloodstain pattern analysis software, 2009.
Andy Maloney, Celine Nicloux, Kevin Maloney, and Franck Heron.One-sided impact spatter and area-of-origin calculations.Journal of Forensic Identification, 61(2):123–135, August 2011.
Kevin Maloney, Jim Killeen, and Andy Maloney.The use of hemospat to include bloodstains located on nonorthogonalsurfaces in area-of-origin calculations.Journal of Forensic Identification, 59(5):513–524, April 2009.
Mega Speed.High-Speed B/W & Color CMOS Camera Model MS50K & MS55K,2.9 edition, 2010.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 34 / 35
References
Luis Zarrabeitia, Dhavide Aruliah, and Faisal Qureshi.Extraction of blood droplet flight trajectories from videos for forensicanalysis.Algarve, Portugal., February 2012. International Conference onPattern Recognition Applications and Methods.
Raquel Murray (UOIT) Modelling Blood Droplet Flight August 23, 2012 35 / 35