Teaching

In our research group, we have several seminars, group meetings, and continuing education events. This includes a weekly research group meeting (Monday 10:00-11:00), interdisciplinary reserach and educational presentations in the department of radiation oncology (Friday at 13:15-14:00), and seminar presentations that happen occasionally. Students doing a master thesis in our group are expected to participate, which will be considered equivalent to the 2 ECTS research seminar.  

(core elective module for the UZH physics master with biological and medical physics specialization)

(recommended elective module for the ETH biomed. eng. master with medical physics specialization)

The course specializes on the mathematical and physical foundations of treatment planning for radiotherapy. The class has two main parts:

1. Interactions and dose calculation algorithms (the physics part)

For both photons and protons, we discuss the relevant interactions of radiation in tissue. Based on that, we derive dose calculation algorithms that calculate the 3D distribution of deposited energy in the patient. In the class we discuss pencil beam algorithms for photons and protons, and the convolution-superposition algorithm for photons.

2. Treatment plan optimization (the mathematical part)

Building on dose calculation algorithm, treatment planning amounts to determining the optimal incident fluence to irradiate the tumor but minimize radiation dose in healthy tissues. We discuss how treatment planning for intensity-modulated radiotherapy with photons (IMRT) and protons (IMPT) can be formulated and solved as a mathematical optimization problem.

During the exercises, students will implement the main components of a radiotherapy treatment planning system in 2D in Matlab.

(recommended elective module for the UZH physics master with biological and medical physics specialization)

New class since the spring semester 2023!

The class uses advanced topics in medical physics and radiation oncology to introduce mathematical concepts and methodologies that have very widespread applications in entirely different fields. We class will consider topics including proton dose calculation, tumor control und normal tissue complication probability models, fractionation decisions, and target volume definition in radiotherapy. Using these applications, an introduction to monte carlo simulations, statistical machine learning, bayesian networks, markov decision processes and optimal control is provided. As such the class is addressed to students with interest in computational methods and their applications to improve cancer treatment. 

The lecture spends a similar amount of time on discussing the application and on introducing the corresponding methodology. Some of the topics are motivated by ongoing research projects. However, the focus of the class is on basic concepts and methods rather than specific research projects.

The lecture (PHY475, 3 ECTS) is associated with computational exercises (PHY476, 3 ECTS). It is possible to only attend the lecture.

Syllabus:

The first part considers fractionation decisions in radiotherapy. Fractionation means that the total radiation dose is not delivered at once but is split into several fractions delivered over multiple days or weeks. Fractionation represents, along with minimizing dose to normal tissues, the most important concept to reduce side effects of radiotherapy. In the context of image-guided radiotherapy at the MR-Linac, we consider the concept of adaptive fractionation. Here, we aim to exploit day-to-day variations in the tumor location by delivering a larger dose on days when the tumor is further away from the most critical organ. The problem of determining the optimal dose to deliver each day can be formulated as a markov decision process and solved via the dynamic programming algorithm - concepts that are fundamental to the field of control theory, sequential decision making, and reinforcement learning.

The second part of the class considers the problem of determining tumor prescription doses and normal tissue tolerance doses for treatment planning. This is done through tumor control and normal tissue complication probability models derived from clinical outcome data. In this context, basic concepts of likelihood inference will be introduced and applied.

The third part introduces the problem of target volume definition, i.e. defining the volume that should be irradiated. While parts of the tumor can be detected using imaging techniques such as CT, MRI and PET, microscopic spread of the tumor cannot be visualized using in-vivo imaging techniques. In the context of developing models to quantify metastatic spread of tumors through the lymphatic system, an introduction to Bayesian networks is provided, which represents a widely applicable statistical machine learning technique for probabilistic reasoning and modeling of joint probability distributions. In the context of developing models for quantifying spread of tumors into adjacent tissues, we consider reaction-diffusion models - a class of partial differential equations that plays a role in the field of nonlinear pattern formation.

The fourth part of the course considers dose calculation for proton therapy. The most accurate dose calculation algorithms are based on monte carlo techniques that simulate the stochastic transport of a large number of individual protons through the patient based on cross sections of the physical interactions. Thereby, tissue heterogeneities can be accurately accounted for, overcoming the limitations of pencil beam algorithms.