P Chelle (1,2), C Morin (1), M Piot (2), A Montmartin (3), N Durrande (1), R Leriche (1), S Laporte (2), X Delavenne (2), E Ollier (2), S Avril (1), B Tardy-Poncet (2,3), M Cournil (1)
(1) Center for Health Engineering, UMR 5307, Ecole Nationale Supérieure des Mines de Saint-Etienne, 42023 Saint-Etienne, France; (2) EA3065, Université Jean Monnet, 42023 Saint-Etienne, France ; (3) Inserm CIC1408, CHU de Saint-Etienne, 42023 Saint-Etienne, France
Objectives: Hemophilia A (HA) is the deficiency of coagulation factor (f) VIII and leads to bleeding tendency. Thrombin Generation (TG), a global PD test of coagulation, may improve management of HA patient substitutive treatment. It describes the thrombin concentration, [IIa](t) in a plasma sample and is well correlated with bleeding severity [1]. TG mechanistic model might be a good way to use this biomarker for the prediction of fVIII to reach. The objective is to evaluate the predictive potential of a set of mechanistic numerical models [2-7] to identify if they might be used to predict TG in HA patients.
Methods: Mechanistic models describe the evolution of concentrations of the plasmatic species interacting in the system by stiff non-linear Ordinary Differential Equations (ODE) system. ODE were implemented in Matlab and solved numerically using ODE15s solver due to ODE stiffness giving [IIa](t). Then, the area under the curve called Endogenous Thrombin Potential (ETP) is calculated from [IIa](t): ETP=∫∞t=0[IIa](t).dt and compared with ETP obtained from a study including N=40 HA patients. Estimated ETP from patient i is noted eETPi and corresponds to the model response to this patient data. Mean Squared Error (MSE) was used to assess the model estimations as well as Stone-Geisser criterion (Q2) a normalized version of MSE [8].
Q2=1-∑Ni=1(eETPi-ETPi)2⁄∑Ni=1(mETPi-ETPi)2
where mETPi is the mean of the N-1 ETP values when ETPi is omitted. Thus, models with good estimations have Q2 close to 1. If Q2 is negative, using the model is worse than using mean to predict data. To minimize bias, optimization of MSE was realized using genetic algorithm (GA) [9] and gradient method (data not shown).
Results: MSE and Q2 results indicate a poor quality prediction for all the original models (cf Table). For mechanistic models, number of interactions is not necessarily synonymous of better behavior. Best estimations are obtained with models having fewer parameters as Panteleev model [6].
Table: Model performance
| Reference | Nb of reactions | Nb of parameters | Q2 | Optimized Q2 | √MSE (nM.mn) | Optimized √MSE (nM.mn) |
| Hockin [2] | 27 | 42 | -1.08 | 0.37 | 552 | 304 |
| Bungay [3] | 46 | 105 | -1.69 | -0.20 | 628 | 419 |
| Tyurin and Khanin [4] | 50 | 72 | -3.29 | 0.04 | 792 | 376 |
| Panteleev [6] | 51 | 65 | -1.94 | 0.51 | 656 | 269 |
| Zhu [5] | 55 | 75 | -8.21 | -0.25 | 1161 | 427 |
| Chaterjee [7] | 57 | 105 | -0.36 | 0.17 | 445 | 349 |
Discussion: The predictive potential of mechanistic models is not good enough yet to predict TG in HA patients. Optimization has given significant improvement on ETP estimations. Over-parameterization of models might explain the lack of precision of these models.
References:
[1] Hemker HC, Giesen P, Al Dieri R et al. Calibrated Automated Thrombin Generation Measurement in Clotting Plasma.Pathophysiol Haemost Thromb 2003; 33: 4–15
[2] Hockin M, Jones K, Everse S, Mann K. A model for Stoichiometric Regulation of Blood Coagulation. Journal of Biological Chemistry 2002; 277 (21): 18322–18333
[3] Bungay S, Gentry P, Gentry R. A mathematical model of lipid-mediated thrombin generation. Mathematical Medicine and Biology 2003; 20: 105–129
[4] Tyurin K, Khanin M. Hemostasis as an optimal system. Mathematical Biosciences 2006; 204: 167–184
[5] Zhu D. Mathematical modeling of blood coagulation cascade kinetics of intrinsic and extrinsic pathways in normal and deficient conditions. Blood CoagFibrinol 2007; 18: 637-646
[6] Panteleev M, Balandina A, Lipets E et al. Task-Oriented Modular Decomposition of Biological Networks: Trigger Mechanism in Blood Coagulation. Biophysical Journal 2010; 98: 1751–1761
[7] Chatterjee MS, Denney WS, Jing H, Diamond SL. Systems Biology of Coagulation Initiation: Kinetics of Thrombin Generation in Resting and Activated Human Blood. PLoS Comput Biol 2010; 6(9): e1000950. doi:10.1371/journal.pcbi.1000950
[8] Wold H. Partial Least squares, In: Kotz S, Johnson NL.(Eds), Encyclopaedia of statistical sciences (1985). vol 6. Wiley, New york, pp 581-591.
[9] A. R. Conn, N. I. M. Gould, and Ph. L. Toint. “A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple Bounds”, SIAM Journal on Numerical Analysis, Volume 28, Number 2, pages 545–572, 1991.
Reference: PAGE 24 () Abstr 3335 [www.page-meeting.org/?abstract=3335]
Poster: Drug/Disease modeling - Other topics