Simulating how the liver works

What does a liver have to do with the Institute of Statics and Dynamics of Aerospace Structures? Tim Ricken, professor and head of the Institute at the University of Stuttgart, has a plausible explanation: “Although the ISD focuses on mechanics, its foundations and tools can also be applied to multi-physical issues such as biomechanics.” This includes the functioning of the liver, which is represented by a blue plastic model sitting on the table in front of Ricken.

The aerospace engineer views the liver as a porous structure filled with blood vessels that transport nutrients and waste in and out. “The basic idea is to create a digital twin of the liver,” explains Ricken. “This will allow us to not only gain more knowledge about how it works but also develop new surgical techniques and achieve a better match in liver transplants. We can also reduce the number of animal experiments required to develop new medicines.”

Architecture of liver

On the left you can see how the structure of the liver and how it is supplied with blood. On the right is a magnified view of the blood supply to a liver lobule. The smallest unit is a single liver cell (hepatocyte).

Stages of Liver Desease

Progression of liver diseases with presentation of the projects currently being funded at the Institute. On the left a healthy liver, second picture from the right liver cirrhosis and on the far right hepatocellular carcinoma. In these two final stages, the disease is fatal and only a transplant can help.

Decision-making tool for liver transplants

Liver transplantation is often the only treatment that can effectively cure end-stage liver disease. Demographic changes and Western lifestyle are leading to a steady increase in the number of chronic liver diseases. An increasing number of elderly recipients and donors have multiple pre-existing conditions. The livers of such donors often do not fully meet the criteria for ideal donor organs.

"A liver that is donated must always match the recipient’s body. Because there are too few donor organs, we must ask whether a liver that isn’t ideally suited could still be used,” explains Ricken. This could increase the number of possible donors. “A liver that was rejected because of its condition would then still be medically suitable for certain recipients.”

Marginal transplants are organs that don’t meet all the criteria for ideal donors because they are affected by pre-existing diseases.

Diseases such as hepatic steatosis (i.e., fatty liver disease) greatly affect the quality of a donor organ. The disease changes the tissue structure, thereby restricting blood circulation and negatively affecting liver metabolism and organ function. In the case of a marginal transplant, the surgeon is faced with the decision of whether to accept or reject the organ. If they reject it, the risk of death increases for those on the waiting list.

Ricken and his team are developing a clinical tool to help physicians diagnose diseases, predict outcomes, and make treatment decisions. The tool is based on the biomechanical model of a liver lobule, the functional unit of the liver. It can be used to simulate perfusion (i.e., the flow of blood through the liver tissue).

Simulation results of a group of seven liver lobules

Nutrient storage after 1610 seconds simulation time. First column: Contour plot for FFA (FFA = free fatty acids) concentration. Second column: Contour plot for oxygen concentration. Third column: Contour plot for fat fraction. (a) Undisturbed distribution, (b) Outflow obstruction, (c) Outflow obstruction with permeability (from Lambers et al. [2024]).

Co-design with physicians and systems biologists

This model is then fed with clinical data such as weight, height, and age as well as liver markers (i.e., proteins used to assess liver health). In addition, the model will be expanded to include data on cold ischemia time and reperfusion damage. Transport time plays a key role here. Because each liver has a different condition, it must also be perfused differently (i.e., blood circulation must be restored). “With this knowledge-based computer model, we want to compare the condition of the donor liver and the condition of the recipient and find a better match,” says Ricken.

Two major challenges in marginal liver transplants are the storage period between organ procurement and transplantation (cold ischemia period), during which the liver is not supplied with blood, and the damage after reperfusion, when the vessels are supplied with blood again and “inflated”.

To determine what to model, the scientists collaborate with experts from the university hospitals in Jena and Leipzig. “We meet regularly with our clinical partners who then tell us exactly what the models must be able to do and what inputs and outputs there are,” explains Lena Lambers, who led the “Biomechanics” working group at the ISD. “The input from the clinic helps us to determine the issues that will be solved with our digital twin. For example, where there are problems or what parameters are important for a liver to match with a foreign body,” says Ricken. The co-design involves not only communication between engineers and medical doctors but also collaboration with systems biologists at Humboldt University and Charité in Berlin. These simulate cell-level behavior using differential equations.

These models can be highly complex with hundreds of equations that must be solved simultaneously for just a single cell. “Many processes occur within it, and depending on where a liver cell is located, it performs different functions and is therefore differentiated accordingly. To understand this, we must first understand how the liver is structured. It’s a porous medium,” says Ricken.

Multi-scale simulations take data from different levels or size scales into account. At the micro level, this involves the interaction of individual organ cells with blood. These cells are in contact over an area of about half a millimeter. At the meso level, it involves blood flow through individual organs, and at the macro level, it involves blood flow through the entire body.

Individualized models

In another project, the scientists are developing a model to simulate tumor growth in the liver. The goal is to create individualized patient prognoses. For this purpose, they again consider a liver lobule as a functional unit to simulate the blood flow through the liver. “We then linked this to other scales such as blood flow throughout the organ or liver cell function with processes throughout the body,” says Lambers.

They first developed a knowledge-based model and fed it with initial clinical data. “The next step is to extend this model further, particularly in terms of clinical usability.” Individual patient data such as tumor volume, previous diseases, and blood pressure are now to be included in the model. This should make it possible to create personalized simulations.

Surrogate models are mathematical models that closely mimic the behavior of the simulation model. With the help of machine learning and neural networks that take physical laws into account, surrogate models are trained with data and results from the simulation. This provides simplified models that can make accurate predictions in a much shorter time.

Real-world test for real-world verification

The scientists also collaborate with partners from experimental and clinical surgery at the university hospitals in Jena and Leipzig. “One problem with our models is that they still take a long time to calculate for real clinical applications,” says Lambers. It may take hours—or even days—to achieve results. The scientists have therefore developed surrogate models that can be calculated more quickly and easily.

To test whether the models can perform under real-world conditions, they will be subjected to a proof of concept trial. “We imagine the surgeon treats the patient as usual in clinical practice. The idea is that another person uses the model to predict the result and compares it with the actual outcome,” explains Lambers.

Staging system for the assessment of liver tumors

Together with Hans-Michael Tautenhahn, a surgeon at the University Hospital Leipzig, who performs many liver transplants himself, the scientists are further developing a staging system. This can help clinicians better assess a patient. “When it comes to tumor formation and treatment of the liver, the University Hospital in Leipzig has a tumor board. Different doctors from different disciplines of the clinic come together and discuss a patient,” Tim Ricken. “We are now carrying out such a simulation as an example for certain patients.”

The doctors can then look at the results of the simulation. “We also have practical questions. For example, how do we present the results? When we conduct a simulation like this, millions of data points are involved. These include simulation images of flows and functional maps across different scales,” says Ricken. “What data can the medical doctors use at all? Can they even read it? How can they read it? And how fast must it go?”

Prototype of a simulation-based scoring system to support clinical therapy decisions

Patient-specific data on the geometry of the liver and metabolism are integrated into the simulation. The system supports doctors in the assessment of a patient.

For example, the staging system could use different colors from green to yellow to red to classify patients. The simulations are designed to refine it so that forecasts can become more accurate and can be used in decision making. “But there is still a long way to go,” says Ricken. That’s because before such a system can be widely used, it must be certified. “The USA is already a lot further ahead. There is already a specific procedure in place for carrying out a certification process with the help of digital twins or numerical simulations according to the American health authorities.

However, this does not yet exist in Europe. The fact that we don’t yet have a regulated procedure for this is actually a hindrance from the authorities.” Ricken expects that it could be 20 years or more before this procedure can be used in the clinics. “But we now have the first steps and the first prototypes. I already have hope that it will be used in the clinic during my time of work—at least as a prototype.”

Manuela Mild | SimTech Science Communication

Project participants

Uta Dahmen, Experimental Surgery, Jena University Hospital
Matthias König, Systems Biologist, Humboldt University of Berlin
Hans-Michael Tautenhahn, Deputy Head of Hepatobiliary Surgery, and Visceral Transplantation, University Hospital Leipzig

About the scientists

Lena Lambers headed the Computer-Aided Biomechanics working group at the Institute of Statics and Dynamics of Aerospace Structures at the University of Stuttgart. She often told her friends and family that she was researching liver simulation and explained that the basic mechanical concepts were the same regardless of whether simulating concrete, flowing water, a porous airplane wing, or a liver through which blood flows. The combination of engineering sciences with medicine and biology gives her the meaning behind her work. Lambers studied civil engineering at the TU Dortmund and then earned her doctorate with SimTech in the project PN 2-2A. She now works as a science manager for research infrastructures at the German Aerospace Center (DLR).

Tim Ricken is Professor and Head of the Institute of Statics and Dynamics of Aerospace Structures at the University of Stuttgart. The liver has fascinated him for over 20 years, and his research motivates him to help people and save lives. He studied civil engineering at the University of Essen and earned his doctorate in mechanics. During a coffee break at the University Hospital Essen, he met the doctor Uta Dahmen, who at the time worked in transplant surgery and told him about the liver, which is a porous medium. Because he had obtained his doctorate in porous media, the successful collaboration, which has now lasted over 20 years, began. Ricken is involved in several projects in SimTech.