Neuroscience and Applied Mathematics

A new mathematical method reads the brain and reveals patterns in brain activity

Research conducted by DTU Compute and Rigshospitalet shows that by using better mathematics, we can begin to see the brain not just as separate parts, but as a dynamic system with shifting patterns. It is another step towards understanding how the brain works – and, in the long term, how to treat it more precisely.

Photo by Shawn Day on Unsplash
The illustration conveys a key idea: that data are not just random points, but have a particular shape or structure. Here, this structure is shown as spheres. The small dots in the background represent the data. The green and red points show two different states that the brain switches between. First, the brain is in the green state for a period of time, after which it shifts to the red state. Each state corresponds to a specific pattern in brain activity. This is illustrated by the different orientations: the green structure is more vertical, while the red is more horizontal. This shows that the two states are distinct. To describe the data correctly, the model must have the right level of complexity. If the model is too simple, it cannot distinguish between the states. If it is too complex, it risks describing random variation rather than meaningful patterns. The goal is therefore to find the right balance, so that the model fits the data. When achieved, the result is a model that both explains the data well and remains interpretable.
The illustration conveys a key idea: that data are not just random points, but have a particular shape or structure. Here, this structure is shown as spheres. The small dots in the background represent the data. The green and red points show two different states that the brain switches between. First, the brain is in the green state for a period of time, after which it shifts to the red state. Each state corresponds to a specific pattern in brain activity. This is illustrated by the different orientations: the green structure is more vertical, while the red is more horizontal. This shows that the two states are distinct. To describe the data correctly, the model must have the right level of complexity. If the model is too simple, it cannot distinguish between the states. If it is too complex, it risks describing random variation rather than meaningful patterns. The goal is therefore to find the right balance, so that the model fits the data. When achieved, the result is a model that both explains the data well and remains interpretable. Credit: Anders Stevnshoved Olsen, DTU/Rigshospitalet

Data from brain scans during tasks

The researchers did not perform the scans themselves. Instead they analysed data from a publicly available dataset in which healthy participants completed seven different tasks and data from so-called resting-state to compare the results of using the methods.

The functional brain scans data is made by scanner continuously takes images of the brain and measures small changes in blood flow, which reflect brain activity. By linking the timing of tasks to these measurements, it becomes possible to see which areas of the brain are active – and how they work together over time.

A key element of the new method is that it moves away from focusing solely on the amplitude of brain signals – that is, the strength of their waveforms. These are highly sensitive to noise, for example if the patient moves during the scan, and can therefore be misleading and not reflect the actual neural signals in the brain.

Instead, the method analyses how signals oscillate together (phase coherence). This provides a more robust picture of how different brain regions interact.

The method is based on a statistical model (a mixture model) of such phase coherence time-series, which describes the brain as continuously switching between different ‘states’ of activity. These states can be identified automatically from the data – without prior knowledge of what the person is doing.

“By modelling the evolution of these oscillations as movement between a mixture of different ‘states’, we have shown that our method is better at detecting when a person is performing a given task in the scanner, and at distinguishing between different tasks than traditional methods,” says Anders Stevnhoved Olsen.

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Facts

The dataset

Brain scans can be acquired while participants are at rest, a so-called resting-state condition. In this study, however, the participants carried out a variety of tasks during the scans.

The study uses data from the Human Connectome Project, which includes seven standardised tasks:

  • Emotion processing
  • Gambling
  • Language
  • Motor (movement)
  • Relational processing
  • Social cognition
  • Working memory

A contribution to personalised medicine

As previously mentioned, the research here focused on methods for mapping how the brain works. This knowledge holds significant potential.

By uncovering how different parts of the brain interact, the method suggests that, in the future, there may be less need to rely on traditional diagnostic categories.

“In the long term, this kind of knowledge could contribute to personalised medicine. For example, if a brain scan shows that a patient’s brain network differs from the typical pattern in a specific way, it may be possible to assign that patient to a group where a particular treatment is more effective,” says Anders Stevnhoved Olsen.

Psychiatric conditions are often difficult to divide into clear categories, and current diagnoses – such as depression, anxiety or stress – are, in many cases, relatively broad classifications.

“It may turn out that the brain changes in patterns that cut across established diagnoses, and which can only be detected using more precise analyses,” he says.

Today, Anders Stevnhoved Olsen works at postdoc at Rigshospitalet on research into consciousness, including studies of patients in a coma:

“In this context, it is highly relevant to be able to describe how brain function differs from that of healthy individuals. That is also something we hope the method can be used for.”

Read more in the scientific journal PNAS.

Facts

The research – Uncovering dynamic human brain phase coherence networks published on PNAS – introduces a new method for analysing the brain’s networks in fMRI data.

Rather than measuring signal strength, the method analyses how signals oscillate together (phase coherence). This provides a more robust picture of how different brain regions interact.

The method is based on a statistical model (a mixture model) that describes the brain as continuously switching between different ‘states’ of activity. These states can be identified automatically from the data – without prior knowledge of the task being performed.

When applied to real brain scans, the model can:

  • identify recurring patterns in brain activity
  • distinguish between different tasks
  • generalise to new individuals