After completing her PhD in Austria and postdoctoral research in Munich, Vanja Nikolić joined Radboud University in Nijmegen in 2019. She is on a path to becoming an associate professor and teaches both undergraduate and postgraduate students. Her current research focuses on using mathematical models to understand ultrasonic waves. 'These waves, for example, assist doctors in viewing the body during prenatal ultrasounds. They can also be used for treating tumors, avoiding the need for surgery.'
Working with mathematical models
Vanja works with mathematical models that describe various phenomena. 'I specialise in models that capture non-linear ultrasonic waves. Many colleagues primarily conduct research in laboratories in this field. We document what we observe in the lab on a computer. This enables us to explore basic principles in a simulation environment, which is also cost-effective.'
Non-linear waves
Sound travels as a wave, similar to water waves. 'The sound you hear when I speak is almost identical to the sound I produce. This is an example of linear sound behaviour. However, non-linear waves can change shape as they propagate,' explains Vanja. 'Such interesting phenomena occur naturally in ultrasonic waves. They have very high frequencies, making them inaudible. These waves are utilised in various medical applications, both diagnostically and therapeutically. The most well-known example is creating images of the body, such as in prenatal care.'
Research into medical applications
One of the intended applications of ultrasonic waves is cancer research, potentially eliminating the need for mammograms. Scientists from different disciplines are working on this. Another research area is their use in tumor therapy. 'Therapeutically, we can use ultrasonic waves to destroy tumors. Focused ultrasound can generate high pressure and heat tissue, reducing or destroying cancer cells,' Vanja explains. 'The advantage is that it is painless, non-invasive, and can be repeated frequently.'
Constantly generating new questions
'My research constantly generates new questions about the underlying ultrasound models, especially in the context of the mentioned applications. There are always potential improvements to discover, which is one of the reasons we do this work. There are always questions to ask and answer.'
Solving mathematical puzzles
'When I started, there were many mathematical challenges in our field. Some of those theoretical questions have been answered. I am proud of that,' says Vanja. 'An important milestone was that we can now capture how non-linear ultrasonic waves depend on the properties of the medium they travel through. We could demonstrate a certain continuity when waves travel through different media. In mathematics, answering open questions is always fascinating. It's like solving a puzzle. The reason we do this theoretical research is to create a comprehensive understanding of ultrasound. We want to generate a complete picture that will also assist other researchers and laboratories in the long term. We aim to establish something that contributes to a deeper understanding of the field.'
Increasing efficiency
Obtaining a fundamental understanding of the underlying mathematical models is very important. Vanja: 'It contributes to more efficient use, enabling us to make computer simulations more reliable and efficient. It brings them closer to the real world.'
Inspiring and motivating students
'Another beautiful aspect of my work is interacting with students and sparking their interest in mathematics. Engaging with students who conduct research and develop a passion for the subject is a wonderful part of my job.' Vanja concludes: 'And sometimes students come up with ideas that I hadn't thought of myself. I find that amazing!'
This interview was previously published on TechGelderland.nl.
