Computational Transport Oncophysics

Cancer is an extraordinarily complex disease. It is now recognized that methods commonly used in physics can help reducing the complexity of cancer to a manageable set of underlying principles and phenomena [1, 2]. Physical properties of biological barriers control cell, particle, and molecule transport across tissues and this transport and its deregulation play an overarching role in cancer physics. According to [1], tissue invasion is mass transport deregulation at the interface between the cell and the microenvironment; metastasis is a deregulation of local and distant cellular transport at the scale of the organism; tumor-associated angiogenesis completely alters mass and fluid exchange across the microcirculation; alterations in the signaling pathways that accompany the evasion of apoptosis, growth signal dependence and growth inhibitory messages from the immediate environment are also disruptions in molecular transport since molecular signaling depends directly on the transport of signaling molecules. Transport aspects control delivery of therapeutic agents (e.g. chemotherapeutics or molecularly targeted therapeutics such as T cells, antibodies, particles) which must pass through different and heterogeneous tumor and healthy compartments (e.g. vascular, stroma) with distinct physical properties [3, 4]. Delivery of drugs is an extremely complex procedure involving different spatial and temporal scales and taking place over several levels ranging from the organism to the intercellular environment. The underlying transport phenomena at individual tumor compartments may act as transport barriers possibly contributing to poor survival rates in cancer therapy [5]. The Mononuclear Phagocyte System (MPS) belongs to these barriers, removing foreign substances from the body such as Nano Particles (NP) in the blood plasma. A second obstacle is given by the tumor neovasculature, which is tortuous, distorted and shows large fenestrations, leading to poor perfusion of the tumor tissue, chaotic blood flow and uneven supply of nutrients [6]. Another barrier is related to transport of drug molecules and carriers through the walls of the capillaries in the tumor tissue: because of the limited drainage of interstitial fluid, its pressure rises reducing the extravasation of therapeutic molecules through advection [7]. Poor perfusion in the local tumor environment hinders diffusion of therapeutic agents in the pores of the extracellular matrix and affects ultimately the cellular uptake of NP [8]. This uptake occurs generally through endocytosis; only successively the payload may be released into the cytoplasm. The concept of biological barriers and their effect on transport has brought a new understanding of how transport can modulate cancer biology and therapeutic efficacy [2]. In fact, several studies [9-12] have confirmed the above hypothesis that transport plays a crucial role in cancer and drug delivery, including resistance [1, 3, 13-15]. Transport Oncophysics views hence cancer as a disease of multiscale mass transport deregulation involving biological barriers [1]. Computational Transport Oncophysics provides the computational tools which, together with imaging, analysis and quantification, will contribute to rationalize the delivery of therapeutic agents forming an oncophysical modeling framework. This framework should complement classical tools used to study pharmacokinetic (PK) and efficacy relations, and create novel precision tools to rationally tailor individual treatments of patients.

Models based on physical laws of transport incorporate fundamental physical relations such as balance laws of mass, momentum, energy and entropy and are quite general. Many parameters for individual lesions can then be obtained from direct observation through suitable imaging techniques. Among these parameters are the blood flow velocity, shear stress at the vascular wall, vascular permeability, and the density of the specific antigens of interest that are expressed on the vascular endothelium [1]. Other parameters needed for the constitutive relations such as the interfacial tensions, mechanical properties of cells, parameters for growth and necrosis have to be obtained from laboratory tests, e.g. [16, 17].

The continuum model for tumor growth including angiogenesis developed by Prof. Bernhard Schrefler (University of Padua and Houston Methodist Research Institute) and co-workers is a very general multiphase flow model in the extracellular matrix (ECM), described as a porous solid; it comprises three fluid phases, i.e. tumor cells (TCs), divided into living and necrotic cells, healthy cells (HCs) and interstitial fluid (IF) [18-24]. The IF transports chemical species such as tumor angiogenic factor (TAF), nutrients and therapeutic agents. Drug transport within extravascular space takes place by convection and diffusion, where tissue glycosaminoglycan content and drug molecular weight are important parameters determining whether extravascular transport is governed by diffusion or convection [25]. Coopted blood vessels are included as line elements with blood flow exchanging nutrients and therapeutic agents with the IF.

The group of the host, Prof. Wolfgang A. Wall (Department of Mechanical Engineering & Munich School of Bioengineering) has ample experience in modeling biological flows (like blood flow in existing vessels) including their theoretically sound connection to homogenized 3D regions as well as in modeling transport and growth processes. Relevant results of the Wall group for this project comprise the work on a multi-scale and coupled fluid-structure interaction and mass transport approach to model biofilm growth [26], the work on coupled poro-elastic modeling [27, 28], the work on developing a realistic placenta model [29] and the huge body of work for modeling the respiratory system [30-36]. Especially the latter body of work on patient-specific reduced-dimensional modeling of complex biological flow and transport, its coupling to 3D domains, the reconstruction of complex vessel geometries from medical images as well as the creation of physiologically realistic networks by a special labyrinthine algorithm constitutes an ideal basis for the project of this Focus Group.

The model which will be developed by Prof. Bernhard Schrefler and the host Prof. Wolfgang A. Wall will couple their respectively developed models for growth of tumors and transport in patient specific vasculature in a unique computational tool. The aim will be to predict the biological distribution of therapeutic agents in tumors following their systemic injection. The distribution of anticancer substances will be used to predict tumor growth and therapeutic response. Imaging, analysis, and quantification of in vivo studies and continuum-level modules are hence the framework that will allow simulating mass transport and biodistribution in the blood stream, the tumor microenvironment and the whole tumor. This will allow for a better understanding of tumor growth and eventually therapeutic efficacy.

1.            Michor, F., J. Liphardt, M. Ferrari, and J. Widom, What does physics have to do with cancer?     Nature Reviews Cancer, 2011. 11(9): p. 657-670.
2.            Moore, N. M., Kuhn, N. Z., Hanlon, S. E., Lee, J. S. & Nagahara, L. A. De-convoluting cancer’s complexity: using a ‘physical sciences lens’ to provide a different (clearer) perspective of cancer. Phys. Biol. 8, 010302 (2011).
3.            Ferrari, M., Frontiers in cancer nanomedicine: directing mass transport through biological barriers. Trends in Biotechnology, 2010. 28(4): p. 181-188.
4.            Ferrari, M., Problems in (nano) medical mechanics. International Journal of Non-Linear Mechanics, 2013. 56: p. 3-19.
5.            Freyer, G., B. Ligneau, B. Tranchand, C. Ardiet, F. Serre-Debeauvais, and V. Trillet-Lenoir, Pharmacokinetic studies in cancer chemotherapy: usefulness in clinical practice. Cancer Treatment Reviews, 1997. 23(3): p. 153.
6.            Carmeliet P, Jain RK 2000 Angiogenesis in cancer and other diseases. Nature 407:249–257
7.            Jain, R.K. Determinants of Tumor Blood Flow: A Review. Cancer Res., 1988, 48, 2641–2658.
8.            Jain RK, Stylianopoulos T 2010 Delivering nanomedicine to solid tumors. Nat Rev Clin Oncol 7:653–64
9.            Godin, B., C. Chiappini, S. Srinivasan, J.F. Alexander, K. Yokoi, M. Ferrari, P. Decuzzi, and X. Liu, Discoidal porous silicon particles: fabrication and biodistribution in breast cancer bearing mice. Advanced Functional Materials, 2012. 22(20): p. 4225-4235.
10.          Pascal, J., E.L. Bearer, Z. Wang, E.J. Koay, S.A. Curley, and V. Cristini, Mechanistic patient-specific predictive correlation of tumor drug response with microenvironment and perfusion measurements. Proceedings of the National Academy of Sciences, 2013. 110(35): p. 14266-14271.
11.          Decuzzi, P., B. Godin, T. Tanaka, S.-Y. Lee, C. Chiappini, X. Liu, and M. Ferrari, Size and shape effects in the biodistribution of intravascularly injected particles. Journal of Controlled Release, 2010. 141(3): p. 320-327.
12.          Godin, B., C. Chiappini, S. Srinivasan, J.F. Alexander, K. Yokoi, M. Ferrari, P. Decuzzi, and X. Liu, Discoidal porous silicon particles: fabrication and biodistribution in breast cancer bearing mice. Advanced Functional Materials, 2012. 22(20): p. 4225-4235.
13.          Ferrari, M., Cancer nanotechnology: opportunities and challenges. Nat Rev Cancer, 2005. 5(3): p. 161--171.
14.          Ferrari, M., The Mathematical Engines of Nanomedicine. Small, 2008. 4(1): p. 20-25.
15.          Ferrari, M., Nanogeometry: beyond drug delivery. Nature Nanotechnology, 2008. 3(3): p. 131-132
16.          Casciari, J. J., Sotirchos, S. V, & Sutherland, R. M. (1992). Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH. Journal of Cellular Physiology, 151(2), 386–94. doi:10.1002/jcp.1041510220
17.          Mueller-Klieser, W., & Sutherland, R. (1982). Oxygen tensions in multicell spheroids of two cell lines. Br. J. Cancer, 256–264
18.          Sciumè, G., S. Shelton, W. Gray, C. Miller, F. Hussain, M. Ferrari, P. Decuzzi, and B. Schrefler, A multiphase model for three-dimensional tumor growth. New Journal of Physics, 2013. 15(1): p. 015005.
19.          Bao, G., Y. Bazilevs, J.-H. Chung, P. Decuzzi, H.D. Espinosa, M. Ferrari, H. Gao, S.S. Hossain, T.J. Hughes, and R.D. Kamm, USNCTAM perspectives on mechanics in medicine. Journal of the Royal Society Interface, 2014. 11(97): p. 20140301.
20.          Sciumè, G., M. Ferrari, and B.A. Schrefler, Saturation–pressure relationships for two-and three-phase flow analogies for soft matter. Mechanics Research Communications, 2014. 62: p. 132-137.
21.          Sciumè, G., R. Santagiuliana, M. Ferrari, P. Decuzzi, and B. Schrefler, A tumor growth model with deformable ECM. Physical Biology, 2014. 11(6): p. 065004.
22.          Santagiuliana, R., C. Stigliano, P. Mascheroni, M. Ferrari, P. Decuzzi, and B. Schrefler, The role of cell lysis and matrix deposition in tumor growth modeling. Advanced Modeling and Simulation in Engineering Sciences, 2015. 2(1): p. 1-26.
23.          Santagiuliana, R., M. Ferrari, B.A. Schrefler Simulation of angiogenesis in a multiphase tumor growth model, Comp. Methods App. Mech. Engng., 304 (2016) 197–216,
24.          Mascheroni, P., C. Sigliano, M. Carfagna, L. Preziosi, P. Decuzzi, B. A. Schrefler Predicting the Growth of Glioblastoma Multiforme Spheroids using a Multiphase Porous Media Model, Biomechanics and Modeling in Mechanobiology, Online First DOI 10.1007/s10237-015-0755-0
25.          Kojic, M., M. Milosevic, N. Kojic, Z. Starosolski, K. Ghaghada, R. Serda, A. Annapragada, M. Ferrari, A. Ziemys 2015 A multi-scale FE model for convective-diffusive drug transport within tumor and large vascular networks, Comput. Methods Appl. Mech. Engrg., 294,100–122.
26.          Coroneo, M., L. Yoshihara, W.A. Wall 2014 Biofilm growth: a multi-scale and coupled fluid-structure interaction and mass transport approach. Biotechnology and Bioengineering, 111, 1385-1395
27.          Vuong, A.-T., L. Yoshihara, W.A. Wall 2015 A general approach for modeling interacting flow through porous media under finite deformations. Comput Methods Appl Mech Eng 283, 1240-1259
28.          A.-T. Vuong, A.-T., C. Ager, W.A. Wall 2016 Two finite element approaches for Darcy and Darcy-Brinkman flow through deformable porous media – mixed method vs. NURBS based (isogeometric) continuity. Comput Methods Appl Mech Eng 305, 634-657
29.          Roth, C., E. Haeussner, T. Ruebelmann, F. v. Koch, C. Schmitz, H.-G. Frank, W.A. Wall 2016 Dynamic modeling of uteroplacental blood flow under IUGR conditions indicates vortices and elevated pressure in the intervillous space, submitted to PLOS Medicine.
30.          Wall, W. A., L. Wiechert, A. Comerford, S. Rausch 2010 Towards a comprehensive computational model for the respiratory system. Int J Num Meth Biomed Eng 26 (7), 807-827
31.          Wiechert, L., W.A. Wall 2010 A nested dynamic multi-scale approach for 3d problems accounting for micro-scale multi-physics. Comput Methods Appl Mech Eng 199 (21-22), 1342-1351
32.          Ismail, M., A. Comerford, W.A. Wall 2013 Coupled and reduced dimensional modeling of respiratory mechanics during spontaneous breathing. Int J Num Meth Biomed Eng, 29 (11), 1285–1305
33.          Ismail, M., V. Gravemeier, A. Comerford, W.A. Wall 2014 A stable approach for coupling multidimensional cardiovascular and pulmonary networks based on a novel pressure-flowrate or pressure-only Neumann boundary condition formulation. Int J Num Meth Biomed Eng, 30 (4), 447-469
34.          Roth, C., A. Ehrl, T. Becher, I. Frerichs, J. Schittny, N. Weiler, W.A. Wall 2015 Correlation between alveolar ventilation and electrical properties of lung parenchyma. Physiological Measurement, 36, 1211-1226
35.          Roth,C. J., M. Ismail, L. Yoshihara, W.A. Wall 2016 A comprehensive computational lung model incorporating inter-acinar dependencies: Application to spontaneous breathing and mechanical ventilation, Int J Num Meth Biomed Eng, accepted, DOI: 10.1002/cnm.2787
36.          Yoshihara,L. , C.J. Roth, W.A. Wall 2016 Fluid-structure interaction including volume coupling of homogenized subdomains for modeling respiratory mechanics, Int J Num Meth Biomed Eng, accepted, DOI: 10.1002/cnm.2812

Publications of the Focus Group


  • Ni, Tao; Zaccariotto, Mirco; Fan, Xuanmei; Zhu, Qizhi; Schrefler, Bernhard A.; Galvanetto, Ugo: A peridynamic differential operator-based scheme for the extended bond-based peridynamics and its application to fracture problems of brittle solids. European Journal of Mechanics - A/Solids 97, 2023, 104853 more…


  • Ni, Tao; Sanavia, Lorenzo; Zaccariotto, Mirco; Galvanetto, Ugo; Schrefler, Bernhard A.: Fracturing dry and saturated porous media, Peridynamics and dispersion. Computers and Geotechnics 151, 2022, 104990 more…


  • Miller, Cass T.; Gray, William G.; Schrefler, Bernhard A.: A continuum mechanical framework for modeling tumor growth and treatment in two- and three-phase systems. Archive of Applied Mechanics 92 (2), 2021, 461-489 more…


  • Gawin, Dariusz; Pesavento, Francesco; Koniorczyk, Marcin; Schrefler, Bernhard A: Non-equilibrium modeling hysteresis of water freezing: Ice thawing in partially saturated porous building materials. Journal of Building Physics 43 (2), 2019, 61-98 more…
  • Peruzzo, C.; Cao, D.T.; Milanese, E.; Favia, P.; Pesavento, F.; Hussain, F.; Schrefler, B.A.: Dynamics of fracturing saturated porous media and self-organization of rupture. European Journal of Mechanics - A/Solids 74, 2019, 471-484 more…
  • Peruzzo, C.; Simoni, L.; Schrefler, B.A.: On stepwise advancement of fractures and pressure oscillations in saturated porous media. Engineering Fracture Mechanics 215, 2019, 246-250 more…
  • Santagiuliana, Raffaella; Milosevic, Miljan; Milicevic, Bogdan; Sciumè, Giuseppe; Simic, Vladimir; Ziemys, Arturas; Kojic, Milos; Schrefler, Bernhard A.: Coupling tumor growth and bio distribution models. Biomedical Microdevices 21 (2), 2019 more…


  • Cao, Toan D.; Hussain, Fazle; Schrefler, Bernhard A.: Porous media fracturing dynamics: stepwise crack advancement and fluid pressure oscillations. Journal of the Mechanics and Physics of Solids 111, 2018, 113-133 more…
  • Kremheller, Johannes; Vuong, Anh-Tu; Yoshihara, Lena; Wall, Wolfgang A.; Schrefler, Bernhard A.: A monolithic multiphase porous medium framework for (a-)vascular tumor growth. Computer Methods in Applied Mechanics and Engineering 340, 2018, 657-683 more…
  • Mascheroni, Pietro; Schrefler, Bernhard Aribo: In Silico Models for Nanomedicine: Recent Developments. Current Medicinal Chemistry 25 (34), 2018, 4192-4207 more…
  • Mikaeili, Ehsan; Schrefler, Bernhard: XFEM, strong discontinuities and second-order work in shear band modeling of saturated porous media. Acta Geotechnica 13 (6), 2018, 1249-1264 more…
  • Ziemys, Arturas; Kojic, Milos; Milosevic, Miljan; Schrefler, Bernhard; Ferrari, Mauro: Multiscale models for transport and biodistribution of therapeutics in cancer. In: Computer Aided Chemical Engineering. Elsevier, 2018 more…


  • Cao, Toan Duc; Milanese, Enrico; Remij, Ernst W.; Rizzato, Paolo; Remmers, Joris J.C.; Simoni, Luciano; Huyghe, Jacques M.; Hussain, Fazle; Schrefler, Bernhard A.: Interaction between crack tip advancement and fluid flow in fracturing saturated porous media. Mechanics Research Communications 80, 2017, 24-37 more…
  • Mascheroni, P; Carfagna, M; Grillo, A; Boso, DP; Schrefler, BA: An avascular tumor growth model based on porous media mechanics and evolving natural states. Mathematics and Mechanics of Solids 23 (4), 2017, 686-712 more…
  • Mascheroni, Pietro; Boso, Daniela; Preziosi, Luigi; Schrefler, Bernhard A.: Evaluating the influence of mechanical stress on anticancer treatments through a multiphase porous media model. Journal of Theoretical Biology 421, 2017, 179-188 more…
  • Milanese, Enrico; Cao, Toan Duc; Simoni, Luciano; Schrefler, Bernhard A.: Fracturing in Dry and Saturated Porous Media. In: Computational Methods in Applied Sciences. Springer International Publishing, 2017 more…
  • Santagiuliana, Raffaella; Pereira, Rui C.; Schrefler, Bernhard A.; Decuzzi, Paolo: Predicting the role of microstructural and biomechanical cues in tumor growth and spreading. International Journal for Numerical Methods in Biomedical Engineering 34 (3), 2017, e2935 more…
  • Schrefler, Bernhard: Computational Transport Oncophysics. Expressions (IACM) 40, 2017, 7-12 more…