A Better Understanding of Brain Tumors

Using an interdisciplinary approach, researchers at the University of Stuttgart build computer models of the dispersal and effectiveness of therapeutic agents used to treat brain tumors. They also seek to solve a fundamental problem of cell biology on the computer: how can patient- specific therapeutic approaches be developed for treating brain tumors?

Brain tumors are a relatively rare type of cancer. The German Cancer Society estimates it represents roughly two percent of all cancers. Nevertheless, brain tumors are especially problematic. Even when they are benign, they can seriously impair the affected patient severely due to the mechanical pressure they exert on brain tissue that is unrelieved in the rigid cranial vault. “As much of a tumor as possible located in an easily accessible area of the brain is first removed surgically. The surgeon tries cause the least amount of damage to the surrounding brain tissue in doing so,” explains Prof. Markus Morrison, director of the University of Stuttgart’s Institute of Cell Biology and Immunology. “This is followed by radiation and chemotherapy. However, to date, curative treatment of a malignant tumor has rarely been achieved.”

A team in the Institute of Applied Mechanics led by Prof. Wolfgang Ehlers, who also is the cluster’s coordinator, is currently attempting to model the dispersal process and distribution of therapeutic agents in the brain. Per Dr.-Ing. Arndt Wagner, a researcher at the Institute of Applied Mechanics, looking at this medicobiological problem from a mechanics perspective is a terrific example of interdisciplinarity. “The dispersal depends substantially on the individual properties of the tissue. This is what we are trying to model.”

A tumor deep inside the brain is not operable and cannot be reached via catheter used in positioning the therapeutic agent next to it. The surgeon consequently must inject the therapeutic into the brain from farther away but so as to let it reach the tumor by the quickest route. If it fails to do so, it will cause unnecessary damage to healthy tissue. “The direct path from the catheter tip to the tumor does not necessarily have to be the geometrically shortest one,“ explains Wagner. “It is how the nerve fibers line up that determines the preferable direction of dispersal.” To put it another way, it may be better the send the therapeutic agent through the brain to the tumor by a detour. “It is this question that we have studied with the help of simulations,” says Wagner.

Therapeutic infusion and spatial distribution within a brain hemisphere during cancer treatment. In the underlying mathematical model, the cells are depicted as a solid object that forms a kind of porous skeleton. Embedded in it are two “cavity systems,” the blood vessels and the interstitial space in which the therapeutic agent disperses. While both are separated from each other by the blood-brain barrier, they still interact through mechanical impulses. The brain model developed at the Institute for Applied Mechanics furnishes a homogenized macroscopic description. What happens at the cell level, on every cell membrane in other words, is not calculable on a scale involving centimeters for the entire brain, because the tissue’s microscopic structure is so complex.

A colleague at the Institute for Applied Mechanics is currently investigating ways of expanding the model to have it describe the therapeutic effect on the tumor. Eventually, that means findings at cell level must be transposed to the entire brain system. This is no small undertaking, as another SimTech project also dealing with patient-specific treatment of brain tumors has shown. “Invariably, many therapeutics work only for a fraction of patients, even when they all have the same diagnosis,” biologist Morrison says. They are intensively researching why this is so, with the additional goal of treating tumors in the future tailored to the individual in optimal fashion.

Morrison goes on to say: “Basic and clinical research have for a long time concentrated on identifying genes and proteins, so that they might predict how patients would respond to certain forms of therapy. It turned out that such data becomes useful only when we allow for the complex interactions of these genes and proteins in mathematical models. Many cellular functions actually only arise on the level of the biological ‘circuits,’ and the same holds true for cell interactions and communications in tissue.” Biologists do basic research to understand how cells process information, how they build signaling networks among themselves, and what therapeutics do with signaling pathways in cancer cells.

Biologists do basic research to understand how cells process information, how they build signaling networks among themselves, and what therapeutics do with signaling pathways in cancer cells. Subsequently, these findings can be transferred to larger systems, for instance, entire affected organs. Researchers like Morrison experiment with this under laboratory conditions – in the petri dish, so to speak. From their results, they can predict the efficacy of different therapeutics for isolated brain tumor cells. Nicole Radde, a professor at the University of Stuttgart’s Institute for Systems Theory and Automatic Control and her team then try to refine the signal transmission models based on the cytological findings. The model’s predictions can then be tested again in the laboratory by an interdisciplinary team.

Prof. Radde focuses especially on developing suitable methods for scale coupling, model identification, and consistent handling of uncertainties. Scale coupling focuses on methods that will succeed in linking microscopic and macroscopic models, i.e., making the transition from cell to organ level. Rade sums up the problem that she and her team often must calibrate with few, highly variable data under the concepts of model identification and handling uncertainties. “When we train our models with these data, naturally uncertainties attach to the predictions,” she explains. “Hence, the question becomes how reliable the predictions based on these models are.”

But it does not mean that unreliable data inevitably yield even more unreliable predictions! “It can happen, for example, that only some variables in the model actually become more uncertain,” stresses Radde, “while others remain fairly independent of the initial uncertainties.” In this context, so-called statistical learning methods offer a powerful tool; however, since they are also very cpu-intensive they must first be optimized.

This is where model reduction methods come into play. Since complex models tend not to lend themselves to being computed in a reasonable timeframe, it is time to call in the mathematicians and informaticians from SimTech, such as the teams around Prof. Guido Schneider from the Institute of Analysis, Dynamics and Modeling or around Prof. Daniel Weiskopf in the Institute for Visualization and Interactive Systems, to ponder new approaches, such as reducing the number of observed parameters in the model elegantly, that is, without sacrificing meaningfulness. Radde has the last word: “Only through this interdisciplinary approach can we even hope to make advances in our research projects.” Michael Vogel