The role of cell lysis and matrix deposition in tumor growth modeling

Background Much research went in the last two decades into the problem of tumor growth and drug delivery [1]. An extensive literature review [2] has shown that the most recent models for tumor growth are multicomponent models with or without diffuse interfaces among the constituents [3–10]. They all consider a malignant mass (tumor cells: TCs), host cells (HCs) and the interstitial fluid (IF) as homogeneous, viscous fluids and employ reaction– diffusion–advection equations for predicting the distribution and transport of nutrients. In general, these models contain limitations on the evolution of the volume fractions and Abstract Background: The multiphase model for tumor growth, proposed by the authors in previous works, is here enhanced. The original model includes a solid phase, the extracellular matrix (ECM) and three fluid phases: living and necrotic tumor cells (TCs), host cells (HCs), and the interstitial fluid (IF). Methods: We introduce the mathematical model for deposition (remodeling) of ECM during the TCs growth, and lysis. Differently from the previous version of the model we take into account that TCs growing in vitro depose their own ECM not present at the beginning. The lysis re-transforms the necrotic cells into IF. The updated mathematical formulation is discretized by means of the finite element method and implemented in a general purpose code. Results: First we reproduce new experimental data of multicellular tumor spheroid (MTS) growth in vitro. The free boundary conditions used in this simulation together with necrosis and lysis allow following the tumor growth curve up to the final steadystate. The second example, by comparing results of tumor growth in an ECM-free medium and in an ECM remodeling medium highlights how ECM deposition affects tumor growth. In an initially ECM-free medium the tumor is unobstructed and can proliferate more rapidly both without ECM and in case of ECM deposition. The third example shows the effect of lysis: it redirects some tumor cells toward the necrotic core of the MTS and produces outflow of the IF from the tumor mass. Conclusions: The introduction of lysis and ECM deposition allows capturing different aspects of the avascular tumor growth not yet comprised in the original model: the MTS growth seems to be influenced by ECM deposition and the lysis seems to be a cause of an outflow of the IF from the tumor mass.