Mathematics as a Bridge from the Laboratory to the Clinic - Importance for Advancing Medicine
Many experimental results only reach patients through mathematical models. The computer scientist Dr. habil. Dirk Drasdo, an expert for simulations in the liver systems biology research network LiSyM, explains how models can contribute to medical advancements in acute and chronic liver disorders.
The doctor says, “We suspect acute liver damage.” Patient X likely ingested an overdose of the painkiller paracetamol. While the patient is still in the emergency department, blood samples are taken and a high-speed tomography is done. All the results are automatically fed into the diagnostics tool Virtual Liver. On entering the patient’s data, the computer then personalizes the mathematical model. A few moments later, Virtual Liver provides a personalized answer to the most important questions: How severe is the liver damage in patient X? Does the pattern of damage correspond to the initial diagnosis? Will patient X recover on his or her own? If not, will it be enough to administer drugs, or should doctors prepare the patient for a transplantation?
Reliable personalized information about a patient’s condition, therapeutic options, and prognosis
This fictional scene is a glimpse of the future. “I’m convinced that we will get there,” says Dr. habil. Dirk Drasdo confidently. A renowned systems biology expert, he is pursuing this goal as a member of LiSyM. “We want to gradually create a virtual liver that can be personalized as much as possible,” he says. As demonstrated by the example, the intention behind the mathematical model is to provide personalized information about the patient’s condition, therapeutic options, and prognosis, without biopsies or invasive surgery being necessary. At this point in time, the focus of the model is on acute forms of intoxication. “We not only have a model for acute cases; in the LiSyM research network, we also recently integrated a model representing how chronic liver damage develops,” says Drasdo, who has a PhD in physics and a habilitation in computer science. “Our simulation is currently based on data from experiments on mice. The next step will be to apply it to patients,” he says. His team is currently working on a model that represents the human condition in various liver diseases.
Models can broaden our understanding of processes within the liver
The model has already broadened researchers’ knowledge of metabolic processes in the liver. After an overdose of paracetamol, the detoxification of ammonia in the liver is severely impaired because the body has trouble metabolizing ammonia. Its concentration in the blood stream increases immensely, which damages the liver severely and can ultimately lead to death. “The common model was not able to explain the ammonia concentration that we were observing,” says Drasdo. Consequently, he and his lab group adjusted a few parameters in their mouse model and added another mechanism. One metabolic path is through the amino acid glutamine. Until now, it was generally regarded as certain that the catalyzed reaction in which glutamate is converted into ammonia by the enzyme glutamate dehydrogenase is irreversible. However, according to the new explanation proposed by the computer models of Drasdo’s team in 2014 , this reaction can go in the reverse direction as well. As they predicted in 2014, in the case of a high concentration of ammonia, an ammonia sink can also occur.
Patients can also profit from the mouse model
“Based on our suggestion, experts from the Hengstler Department at the Leibniz Research Center For Working Environment and Human Factors of the Technical University Dortmund (IfADo) tested this new approach in vivo – in other words, on living organisms,” says Drasdo. The exact mechanism that his team predicted was found in mice. “The scientists from IfADo were able to translate this into a new therapeutic approach,” he says. With this treatment , all of the mice survived after a paracetamol overdose. “This could also work in humans,” says Drasdo.
Many experimental results can only be applied clinically through models
Many experimental results can only reach patients when mathematical models are used. These models take the results from all available sources – in vitro results from test tubes, as well as results from tissue samples, cell cultures, and the entire organism – and combine these to create a useful whole. Also, nobody wants, or is allowed to, poison patients in the name of medicine. “Experiments on the toxicity of substances in humans are not acceptable in most cases,” stresses Drasdo. Researchers therefore turn to other methods. One such approach is the deduction of a real life situation from test tube results. “For us, models that can do this with humans are like the Holy Grail!” says Drasdo. This is because developing and setting up complex models requires so much time and effort. For one, they include countless results from chemistry, physics, biology, pharmacy, medicine, and other disciplines in the form of mathematical formulas. They also require very sophisticated technology, considering that thousands of simulations must be run for some of the steps within the process [see part II].
A chronic path to liver cirrhosis is also included in the model
Drasdo’s mouse-based acute simulation model quantifies the extent of acute damage resulting in the liver from various high doses of toxins. It predicts how well or how poorly the organ will regenerate. However, the regeneration of the liver is completely different after acute damage than after chronic damage. For this reason, Drasdo’s model now also largely represents a chronic path to liver fibrosis in mice. This path represents to what extent repeated overdoses of paracetamol cause the same kind of formation of characteristic spatial patterns of extracellular material deposits that doctors also observe in human patients. To create this path, Drasdo and his lab group at LiSyM integrated many other cell types in the liver into the original model. They also increased the spatial resolution and included the formation and metabolism of certain extracellular matrix proteins into the model. “More than this is probably not necessary at this level,” he explains.
NAFLD is a major health problem in society
Chronic damage to the liver can have different causes – for example, excessive consumption of alcohol over many years, viral hepatitis, or long-term unhealthy eating habits. The latter can cause what experts refer to as nonalcoholic fatty liver disease (NAFLD). Researchers can simulate this condition in the animal model by feeding mice a so-called Western diet, which includes a high percentage of saturated fatty acids. NAFLD is becoming increasingly widespread in the population, meaning this disease is a major health problem in society. In the long term, chronic damage to the liver often leads to fibrosis and cirrhosis of the liver, regardless of its original cause or path of development. While fibrosis of the liver is reversible with appropriate therapies, this is not the case with cirrhosis of the liver. That is why liver experts today express the urgent need for developing tools that can better diagnose, monitor, and treat this disease.
Compromises made when developing a model usually do not pay off
The mouse model can be applied to humans at least partially. “We know from evolution that there are many analogies,” says Drasdo, adding: “For example, we have observed the same damage after paracetamol poisoning in both organisms.” The extent to which this damage corresponds will be demonstrated in further comparisons and in many validations with human material – including, but not limited to, blood markers, biopsy samples, and images from modern imaging techniques. Drasdo hopes to see the first clinical applications in about three to four years. “We are slowly working our way toward the big picture with our modest model versions,” he says. In order to achieve this, he stresses the importance of stable financial support: “In reality, we are constantly chasing after sufficient funds. The ongoing lack of resources forces us to make compromises that often do not pay off in the long run.”
“The goal is the virtual patient”
Drasdo has a clear vision. At some point, he intends for his model to be part of a larger one that encompasses everything from the molecular level to the entire human body. “The goal is the virtual patient,” he says. Therefore, this larger model will not only represent metabolic pathways, changes in cell forms, damage and regeneration after acute and chronic events, as well as other processes of the liver; it must include all organs and processes in the body. This is a major undertaking.
For the moment, Drasdo is focusing on smaller goals for his model. For example, doctors have found that some people die while others recover unscathed after taking the same overdose of paracetamol. At the moment, experts cannot predict which patients will recover and who will not. Consequently, it is important to provide good therapies to avoid fatalities. Drasdo hopes his model will soon contribute to this. The new therapeutic approach identified by his mouse model may someday be applied to humans. As he says, “I would be glad if our model had a positive impact on society – in other words, if it led to one or two applications that offer effective help to liver patients.”
 Schliess, F., Hoehme, S., … D., Drasdo, D., Zellmer, S. (corresponding authors) (2014), Integrated metabolic spatial-temporal model for the prediction of ammonia detoxification during liver damage and regeneration, Hepatology 60 6: 2040–51.
 Ghallab, A., Celiere, …, D., Drasdo, D., Gebhardt, R., Hengstler, J.G. (*senior authors) (2016), Model guided identification and therapeutic implications of an ammonia sink mechanism, J. Hepat 64(4): 860–71.
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