Past Event: Oden Institute Seminar

Supermodeling of a tumor with isogeometric analysis solvers

Maciej Paszynski, Professor, AGH University, Krakow, Poland

Abstract

In this presentation, we show that it is possible to obtain reliable prognoses about cancer dynamics by creating the supermodel of cancer, which consists of several coupled instances (the sub-models) of a generic cancer model, developed with isogeometric analysis [1,2]. Its integration with real data can be achieved by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between sub-models, instead of matching scores (even hundreds) of tumor model parameters as it is in the classical data adaptation techniques. We show that the isogeometric analysis is a proper tool to develop a generic computer model of cancer, which can be used as a computational framework for developing high-quality supermodels. The latent fine-grained tumor features e.g. microscopic processes and other unpredictable events accompanying its proliferation not included in the model, are hidden in incoming real data. The details of the supermodeling algorithm are the following. The tumor growth model involves tumor cells density, tumor angiogenic factor, oxygen concentration, extracellular and degraded extracellular matrices scalar fields, and the vascular network. The progression of the model is controlled by 21 parameters. Our goal is to obtain the progression of the supermodel similar to the one obtained from measurements. We first perform a sensitivity analysis of the tumor growth model, where we identify four more sensitive parameters, namely, tumor cell proliferation time, tumor cell survival time, and threshold oxygen con-centration for tumor cells to multiply or die. Based on the analysis, we set up three different models resulting in different tumor growth evolution. Next, we construct a supermodel by a linear combination of particular models, with coupling parameters obtained by the predictor/corrector technique. We run the three models, and after performing several time steps we correct the resulting fields, e.g. b(1)=C_{12}(b(1)-b(2))+C_{1,3}(b(1)-b(3)), where b(i) is the tumor cell density from model i. Next, we correct the fields by referring to the measurements e.g. b(1)=C_{1,meas}(b_meas-b(1)). Finally, we compute the average oxygen field, b=(b(1)+b(2)+b(3))/3, and we correct the coupling constants c_{i,j}=const*integral(b_meas-b)(b(i)-b(j)), where const is some magic correction constant, selected experimentally. Thus, by using the supermodeling approach we can simulate the reality by a linear combination of different models, and the resulting fields maybe not possible to obtain by any of the single models. This approach is similar to the one already used for climate supermodeling [3]. Acknowledgement. National Science Centre, Poland grant no. 2016/21/B/ST6/01539 [1] Marcin Łoś, Maciej Paszyński, Adrian Kłusek, Witold Dzwinel, Application of fast isogeometric L2 projection solver for tumor growth simulations, Computer Methods in Applied Mechanics and Engineering 316 (2017) 1257-1269 [2] Marcin Łoś, Adrian Kłusek, Muhammad Amber Hassaan, Keshav Pingali, Witold Dzwinel, Maciej Paszyński, Parallel fast isogeometric L2 projection solver with GALOIS system for 3D tumor growth simulations, Computer Methods in Applied Mechanics and Engineering, 343, (2019) 1-22 [3] Frank M. Selten, Francine J. Schevenhoven, Gregory S. Duane, Simulating climate with a synchronization-based supermodel, Chaos 27, 126903 (2017)