Computational sciences used in research against Cancer

What research is your team conducting in this field?

Dirk Drasdo and Wiliam Weens:  Our group is working on various projects and, more generally, on tissue organisation and regeneration, as well as the cancer cell growth processes in the liver and lung.

We were involved in the CancerSys project until 2011. This was an EU project dealing with the early stages of liver cancer development. The experimenters worked in close cooperation with us in order to explain the phenotypes of the tumours observed in the experiments. In these experiments, a molecule was injected into transgenic mice in order to induce the formation of tumours.

We are also working on similar projects on lung cancer in order to assess the growth and invasion properties of small-cell lung carcinoma, a very aggressive form of cancer. The objective is to study the therapeutic options, such as the effects of chemotherapy and erythropoietin (a glycoprotein) using models and experiments.  The experiments and modelling carried out include the processes which occur at different scales - intracellular, cellular and multi-cellular - and consider the various experimental systems: in vitro, mouse and human. Mathematical models are used to guide the experimental strategy towards the most promising and instructive experiments.

Other projects that we are working on address tissue homeostasis* in order to understand the mechanisms underlying the control of cell population growth; the effects of biomechanical constraints on tumour spheroid growth; the effect of certain medication on liver cells in vitro to assess the long-term replacement of in vivo models (animal) by in vitro  systems.

Lastly, we are involved in the virtual liver network project (VLN); see below.

Each project is funded by national organisations in France and Germany, or by the EU. All the projects are conducted in close cooperation with partners (experimenters, modellers and industry). This makes it possible to directly configure the models using experimental data, to validate the model predictions and to include advanced modelling at every scale. Lastly, this pushes us in the direction of research providing added value to companies.

How are computer science and mathematics useful in this type of research?

Dirk Drasdo and Wiliam Weens:

The methods which we use to analyse the source of multicellular organisation combine computer science, mathematics and physics, and mainly use a process chain developed in our group to understand the mechanisms of tissue organisation at the histological level (study of biological tissues). The process chain is well illustrated in the observation of liver regeneration after a toxic and destructive injection.

In order to create realistic simulations, the architecture of the liver was determined at the histological level based on images of optical and confocal microscopy obtained during the injection phase. These images were analysed and made it possible to measure the parameters of the architecture and damage in the lobules, which in turn made it possible to obtain a representative statistical sample quantifying the liver before and after the injection and associated damage.

The results obtained were used to create the initial state of our mathematical model and to configure it for dynamic regeneration. In this model, the blood vessels and hepatocytes (cells that exist only in the liver) are represented.

Model simulations can be seen as "computer experiments", since they are virtual experiments. The results produced by our model are compared quantitatively with the experimental results. Thanks to a sensitivity analysis strategy, by varying each mathematical parameter in a physiologically reasonable domain and by changing the model thanks to numerous exchanges with our experimenter partners, we were finally able to plan a process, unknown and subsequently validated, for liver regeneration.

Our current line of research follows this general outline: definition of spatial parameters based on experimental images, construction of the model, and comparison of the results with experimental data. The processing and analysis of an image, followed by the definition of the parameters of the analysed images, can enable a specialist to objectivize his diagnosis based on independent estimates of histological material. Since we work at the histological scale most of the time, we mainly use agent-based models in which each cell is represented. This type of model consists of two main types:

• models where each cell is characterised by physical and kinetic properties in a continuous space. A cell moves due to the force applied to it, in addition to its own movement (its micromotility). The cells may grow, divide, die, change their polarity, etc., thereby performing all the state changes and activities observed in the experiments.
• rule-based models on non-structured networks, calibrated by the physical model described previously in order to avoid any artifacts caused by an inappropriate choice of rules. The latter type enables work on larger populations for certain models up to a billion cells, but - as is the case in a discrete space - without authorising gradual changes in the cell position. For this reason, we are increasingly supplementing our methods with continuous models where cell equations are not resolved individually, but replaced by local-density variables.

The basic advantage of individual-centred models based on cells is that the molecular signalling intracellular network and the metabolic networks (extensively studied in systems biology over the last decade) can be directly and literally integrated into each cell and coupled to the cell's state and activity. The development of nutrients and signals in the extracellular space is calculated using partial differential equations.

Until October 2011, you were involved in the Cancersys project. Since then, you have been involved in the virtual liver project. What role do you play and what are the issues at stake?

Dirk Drasdo and Wiliam Weens:   Indeed, we are involved in the virtual liver network, which is probably the largest systems biology network that focuses its efforts on a common goal worldwide. The network encompasses all of Germany and we are the only foreign partner. It includes 69 sub-project leaders in various research institutes and universities, as well as in the Bayer company. This great scientific challenge aims to measure and model all processes at all spatial and temporal scales of healthy and diseased livers. This includes the regulation of the expression of genes, the transduction of the intracellular signal, metabolism, intercellular signals, cells of different types and in different states, the functional units of the organ such as the lobules (the smallest functional sub-unit of the liver), the liver lobes, including blood and biliary networks, and finally the organ as a whole and the impact at the patient level.

The processes at each scale must be linked in a way that is appropriate to the process and state of the smaller and greater scales that are consecutive, but not only. This implies serious challenges regarding the development of models at each scale, their integration and the software implementation in order to achieve an integrated model linking all the different components.

The second great challenge lies in the organisation of the communication and progress of the operations, which must be carried out horizontally between the experimenters and the modellers working at a certain scale, and vertically for those working at different scales. Since experimental and modelling methods are often very different from one scale to another, communication between them is a very ambitious task. A management team and a scientific advisory team must be established to coordinate and guide the partners’ activities, thereby enabling the network to progress as a well-orchestrated collective.

In this project, we are responsible for integrated modelling at the lobule and lobe scale, a scale for which we are a referent at the administrative level of the management team.