(436f) Use of 3-Dimensional Response Surface Plots for Heat Transport in the Human Eye to Predict Time of Death

Historically, estimation of time of death in humans has always been a valuable forensic tool.  Over the years, there have been numerous models proposed to estimate time of death [1,2].  Results of these models can be useful to crime scene investigators, but are not strictly admissible into courts of law like DNA analyses, due to much error and variability associated with these current models.
    Most “time of death” models that are developed rely upon torso modeling and rectal temperature profiles.  This approach is untenable since there is too much variability in tissue size and distribution across human bodies in the general population.  Every body is different, so a single reliable a priori model is not practical.  A more reliable approach is believed to be based upon temperature decay in the human eyeball.  The size of the eyeball and distribution of surrounding tissues (skull, brain, etc.) are fairly consistent throughout the human population.
    COMSOL Multiphysics® finite element software program was used to model convective/radiation heat transfer from the human eyeball to the surrounding air.  Postmortem temperature decay curves were collected in eyeballs of several human corpses over a period of 2 - 24 hours.  Of course, each of these curves represent only a portion of the complete temperature decay curve, since the pathologist was able to start collecting temperature data only after some time had elapsed from when the individual had died.  These portions of the actual cooling curves were compared to complete model cooling curves developed with COMSOL.  Theoretically, if a model cooling curve can be superimposed exactly upon the actual cooling curve, time of death can be reliably predicted.  
    Based upon the preliminary results of earlier work [3], 3-dimensional plots have been prepared for constant ambient temperature conditions of 10 - 33 ^oC, for convection/radiation heat transfer coefficients of 7.0 - 13.0 W/m² K, over a period of 0 - 24 hrs.  Given a single constant ambient temperature, a model response surface of eyeball temperature has been generated as a function of time and heat transfer coefficient.  Therefore, there are 24 model response surfaces, each described by a mathematical relationship, to address the range of constant ambient temperature conditions of 10 - 33 ^oC.
    For practical purposes, once a coroner or a medical examiner arrives at the scene, the ambient temperature is recorded and the fact verified that the victim has not been previously exposed to widely varying temperatures.  A recording device is used to record the temperature within the eyeball and the ambient temperature every 5 min for a 1 hr period.
    At this point, the coroner or medical examiner has captured a small portion of the actual postmortem temperature decay curve (PTDC).  This is called the field PTDC.  The 3-dimensional response surfaces generated from the software model is called the model PTDC.  The small response surface of the field PTDC is mathematically matched to the larger comprehensive response surface of the model PTDC.  Once the match is complete, through reverse engineering, the model can be used to extrapolate back to time zero to estimate time of death.
    Sensitivity studies were also performed to evaluate how sensitive is the estimated time of death to variations in ambient temperature conditions and values of the convective/radiation heat transfer coefficient.  

1.  Henssge, Claus, The Estimation of the Time Since Death in the Early Postmortem Period, 2nd Ed., London: Arnold Publishing, 2002.
2.  Smart, Jimmy L, Estimation of Time of Death With a Fourier Series Unsteady State Heat Transfer Model,  J. Forensic Sci, June 2010.
3.  Jimmy L. Smart, Michal Kaliszan. Use of a Finite Element Model of Heat Transport in the Human Eye to Predict Time of Death, J. Forensic Sci, submitted Feb 2011, accepted Jan 2012, published Mar 2013.