Improving cancer treatment simulations with stable, efficient electromagnetic modeling
Pieter van Diepen defended his PhD thesis at the Department of Electrical Engineering on November 13th.
Accurately predicting how electromagnetic waves interact with different materials is essential for applications like hyperthermia, a cancer treatment that uses focused electromagnetic waves to enhance chemotherapy and radiation. However, current computer simulations for these treatments are often too slow. The PhD research of Pieter van Diepen addresses this by exploring a faster simulation method, which is limited by how precisely interaction-matrix elements are computed. By developing techniques to improve stability, his work brings us closer to more efficient and reliable treatment planning.
Electromagnetics is the physics behind the interaction of electromagnetic waves and materials. The propagation of these waves is dictated by the type of material, such as glass or metal, and the shape of the material, like spherical or prism-shaped. Since our day-to-day life includes countless variations in material types and shapes, predicting the behavior of electromagnetic waves can be quite challenging. As a result, computer simulations are necessary to visualize electromagnetic interactions. However, in some applications, the time required for simulations can become excessively long. Examples where these long simulation times are particularly relevant include electronic system vulnerability analysis during and after a nuclear pulse, metalens design for next-gen optics, and hyperthermia. The focus in this research is on the last of these.
Time-domain integral equations
Hyperthermia is the localized heating of tissue to improve the effectiveness of cancer treatments like chemotherapy and radiation therapy. The heating can be achieved electromagnetically, where a set of antennas is used to focus the electromagnetic waves on a specific spot inside the body. The tissue distribution of the human body differs per person. Therefore, every patient requires a personal hyperthermia treatment planning. The planning consists of an MRI or CT-scan to determine the tissue distribution, followed by numerical simulation to compute a suitable antenna operation. To maximize the effectiveness of hyperthermia, computer simulations need to include small details and complex wave-material interactions, resulting in excessively long simulation times. To enable faster planning, research into potentially faster computer simulations is vital. A high-potential candidate is to simulate via time-domain integral equations, which are potentially a thousand times faster than the current de facto standard in hyperthermia treatment planning. The only downside: these simulation methods are unstable. That means that the simulation results are corrupted by non-physical artefacts that obscure the actual electromagnetics.
Faster and more reliable simulations
For his PhD research delved into the causes of instability in these simulation methods. His research showed that the limited accuracy of the calculations performed prior to the actual simulation causes instability. He developed several methods to mitigate the effects of limited accuracy to obtain stable results. He illustrated the improved stability of simulation methods involving materials like metals and the non-conductive part of human tissues. His work is a step closer towards faster and more reliable simulations for applications like hyperthermia.
This work was conducted within the Electromagnetics and Multi-Physics (EMPMC) lab, which is one of the five labs that together form the Electromagnetics group at Eindhoven University of Technology.
Title of PhD thesis: . Promotor: Martijn van Beurden. Co-promotors: Roeland Dilz and Peter Zwamborn.
PhD in the picture
What was the most significant finding from your research, and what aspects turned out to be most important to you?
"I think we've gained a lot more knowledge about time-domain integral equations for electromagnetism. About halfway through the research, we thought the technique was mature enough for practical applications. Unfortunately, that turned out not to be the case after more testing. So, I shifted my focus to understanding what鈥檚 needed to make this technique practically usable."
What was your motivation to work on this research project?
"I studied Electrical Engineering, but during my master鈥檚, I realized that I was most interested in numerical methods (a type of applied math). Since I felt I hadn鈥檛 developed enough expertise in this area after my master鈥檚, I decided to pursue a PhD in this field."
What was the greatest obstacle that you met on the PhD journey?
"The stability of time-domain integral equations for electromagnetism is something of a 鈥榖lack box鈥欌�攜ou put something in, get something out, and then have to figure out what鈥檚 happening inside that black box. It took years for me to develop an intuition for what was really going on and to learn to separate the main issues from the side issues."
What did you learn about yourself during your PhD research journey? Did you develop additional new skills over the course of the PhD research?
"Your perseverance is tested intensely during a PhD. I enjoyed doing the research, but writing was truly a nightmare. Thankfully, I got better at it with a lot of help from the university and my advisor. Now that I鈥檓 working elsewhere, I realize that during my PhD, I learned how to handle complex, abstract concepts and really make them my own. This has helped me start contributing quickly in my new job."
What are your plans for after your PhD research?
"While I get a lot of satisfaction from doing research, I missed the collaborative aspect鈥攕pecifically, the kind where you鈥檙e working closely with someone else to solve a problem together. That鈥檚 why I decided not to stay in academia and to make the shift to industry. I鈥檝e now started as a Metrology Functional Engineer at ASML. Essentially, I work on optimizing machine settings so they print exactly what the customer wants. I鈥檝e found exactly what I felt was missing before."