Quantitative approach to tumor progression and growth

The main goal of the research that I actively contributed to plan and carry on is to understand the dynamics of the tumor microenvironment and thus to unravel the laws that drive tumor progression.

To this purpose, more than ten years ago we decided to attempt developing a comprehensive biophysical model of solid tumors. We soon realized that the task was extremely difficult, but we went on and solve many conundrums. Our true multidisciplinary approach is described here and a list of our published results can also be found on this website.

Basically, we follow a strictly quantitative approach where each step of model development is validated by comparing simulation outputs with experimental data. While this strategy may slow down our advancements, at the same time it provides an invaluable reward: we can trust simulation outputs and use the model to explore territories of cancer biology where current experimental techniques fail. You may read our recent reviews for details:

  • R. Chignola, E. Milotti. AIP Advances, 2012, 2: 011204
  • E. Milotti, M.Sega, S.Stella, F. Dogo, R. Chignola. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2013, 10: 805
  • R.Chignola, M. Sega, S.Stella, V. Vyshemirsky, E. Milotti. Biophysical Review and Letters, 2014, 9: 273

The reasons behind our approach


tumor progression Consider the picture on the left. It is taken from a review by G.N. Naumov, J. Folkman and O. Straume published in the journal Clin. Exp. Metastasis, 2009, 26: 51, and it illustrates the main phases of tumor progression.

At the very beginning there is a single cancer cell. This cell might originate from a normal cells through neoplastic transformation (a rather complex process by which a normal cell becomes a tumor cell). Alternatively, this cell might be a metastasis, i.e. a cell that migrates from an already established tumor

The single cancer cell proliferates and generates a population of cells that form a microscopic solid tumor. The tumor is small and cells can take up nutrients directly from the surrounding medium.

The small tumor stimulates the formation of blood vessels. This key process is called the angiogenic switch. Newly formed blood vessels migrate in the tumor and deliver nutrients to tumor cells. Without blood vessels a solid tumor can grow up to the size of ~1 mm3 and then stops growing because of nutrient restriction; with new blood vessels the tumor starts growing again.

The growth is unlimited. Tumor volume increases exponentially, the network of blood vessels is not regularly organized. Blood vessels can not deliver nutrients to all cells in the tumor and many cells die forming large areas of necrosis. All these steps involve a huge number of different genes and molecular paths to take place, and we now know many fine details. Indeed we try to exploit this knowledge to develop new drugs and stop the different phases of tumor progression.

Becoming quantitative

The picture above shows that tumor progression needs time to occur. But, how long does it take a tumor to jump from one step to the next? We can answer this question. Let us consider the following facts:


We can use the above data and assume that a tumor grows exponentially (as far as we know this is a reasonable assumption). Then, we can calculate the duration of each step of tumor progression for a prototype solid tumor. The result is quite impressive (but not new. Similar considerations were done by J.E. Talmadge in his important review appeared in the journal Cancer Res., 2007, 67: 11471 ):


It takes ~5.7 years for a tumor cell to form a small solid tumor and reach the angiogenic switch stage. This time span might be much longer because of tumor dormancy, a process by which tumor cells apparently stop proliferation but do not die. Approximately 3 more years are needed for a solid tumor to become diagnosable and thus visible to our inspection, and further 2 years to cause patient’s death. The most important conclusion is that more than 80% of the life history of a solid tumor remains hidden. We do not even know that the tumor exists, but during this time tumor cells evolve, new and possibly more aggressive variants are selected and eventually migrate to distant sites to form metastasis. During this long time period a solid tumor can acquire the aggressive phenotype that renders cancer a life-threatening disease.


Tumor progression is a highly dynamic process. How can we stop tumor progression if we can not even observe and understand it?

We can extend the limit of our knowledge by growing tumors in experimental animals, and even beyond that by growing three-dimensional aggregates of tumor cells in vitro (tumor spheroids) to reproduce the biological properties of avascular tumors. However, in these cases it is not easy to take measurements at the appropriate spatial and temporal scales to investigate and understand the dynamics that govern the microscopic world of tumors.

When available, modern techniques force the experimenter to stop the growth process and destroy the cell aggregates to take measurements, and this leaves out the temporal dimension; on the contrary, if time is included in the assays and tumors are left free to grow then no measurements are possible to capture and quantify the fine details of the tumor microenvironment. Fortunately, there are tools to deal with this sort of biological uncertainty principle: present-day computers are powerful enough to tackle quite complex models, such as those that simulate tumors’ behavior at multiple space and time scales.

We believe that there is no golden standard in tumor modeling, so that eventually many different approaches might be required to develop useful models for oncology. In our own simulation program we decided to start with biophysical models at the cellular level. When validated with experimental data these models have been put together to obtain a quantitative in silico laboratory where we can now make interesting and potentially useful exploratory investigations.

Further details at our VBL website