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Math Med Biol. 2009 Dec;26(4):323-36. doi: 10.1093/imammb/dqp011. Epub 2009 May 18.

The impact of uncertainty in a blood coagulation model.

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  • 1Department of Mathematics and Statistics, Center for Complex Systems, Vermont Advanced Computing Center, University of Vermont, Burlington, VT 05401, USA.


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 (w(k(i))(f)(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 (w(k(i))(f)(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.

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