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Mathematical Medicine and Biology Advance Access published online on May 18, 2009
Mathematical Medicine and Biology, doi:10.1093/imammb/dqp011
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

The impact of uncertainty in a blood coagulation model

Christopher M. Danforth

Department of Mathematics and Statistics, Center for Complex Systems, Vermont Advanced Computing Center, University of Vermont, Burlington, VT 05401, USA

Thomas Orfeo, Kenneth G. Mann, Kathleen E. Brummel-Ziedins{dagger} and Stephen J. Everse

Department of Biochemistry, College of Medicine, University of Vermont, Burlington, VT 05405, USA

{dagger} Corresponding author. Email: kathleen.brummel{at}uvm.edu

Received on October 31, 2008. Revised on February 19, 2009. Accepted on April 3, 2009.

Deterministic mathematical models of biochemical processes operate as if the empirically derived rate constants governing the dynamics are known with certainty. Our objective in this study was to explore the sensitivity of a deterministic model of blood coagulation to variations in the values of its 44 rate constants. This was accomplished for each rate constant at a given time by defining a normalized ensemble standard deviation (wFormula(t)) that accounted for the sensitivity of the predicted concentration of each protein species to variation in that rate constant (from 10 to 1000% of the accepted value). A mean coefficient of variation derived from wFormula(t) values for all protein species was defined to quantify the overall variation introduced into the model's predictive capacity at that time by the assumed uncertainty in that rate constant. A time-average value of the coefficient of variation over the 20-min simulation for each rate constant was then used to rank rate constants. The model's predictive capacity is particularly sensitive (50% of the aggregate variation) to uncertainty in five rate constants involved in the regulation of the formation and function of the factor VIIa–tissue factor complex. Therefore, our analysis has identified specific rate constants to which the predictive capability of this model is most sensitive and thus where improvements in measurement accuracy will yield the greatest increase in predictive capability.

Keywords: blood coagulation; uncertainty; math modeling


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