Opportunities for students of operations research, math, physics, computer science who are interested in optimizing cancer therapy, especially in radiation oncology. The projects are suitable as PhD thesis projects, or as part of postdoctoral fellowships. Some may also be suitable for MS theses.

Please contact the person listed next to the project title for further information.


Spatio-temporal optimization (Thomas Bortfeld, This email address is being protected from spambots. You need JavaScript enabled to view it.)

The project considers mathematical optimization problems that arise in radiation therapy for treating cancer patients. Radiotherapy treatments are typically fractionated, which means that radiation dose is delivered over several days or weeks rather than in a single treatment session. In current clinical practice, the total radiation dose is split evenly and the patient is treated in the same manner on every day of the treatment. Recently, we have shown that the effectiveness of radiotherapy can potentially be improved by altering the radiation dose distribution from day to day, a concept that is referred to as non-uniform spatiotemporal fractionation. Designing such treatments, however, is algorithmically far more challenging than designing conventional uniformly fractionated treatments. Conventional treatments are designed based on the physical radiation dose delivered; in the context of fluence map optimization for IMRT or IMPT, this can be performed using large-scale linear and convex optimization algorithms. Designing non-uniform spatiotemporal treatments is based on biologically effective dose, which is a quadratic function of the physical dose. This leads to large scale non-convex quadratically constrained quadratic programming problems (QCQP). The goal of this project is to develop a new set of optimization algorithms that can be used in radiotherapy treatment planning studies to fully assess and exploit the benefit of non-uniform spatiotemporal fractionation for different types of cancer. 


Drug and radiation sensitivity prediction (David Craft, This email address is being protected from spambots. You need JavaScript enabled to view it.)

Cancer is a genetically heterogeneous disease, both across cancer types and within. Nevertheless, most patients are prescribed treatments without regard to any specific biological signatures of their disease. Predicting whether a given drug will be effective, and predicting the side effects that the patient will experience, is not done well for most cancers. This project seeks to use genomic data and curated knowledge of biological pathways (groups of genes that are known to be involved in particular cellular functions) to predict whether or not a patient will do well on a given drug or combination of drugs and radiotherapy. The approach can be summarized as biologically-informed statistical learning.

All candidates should have some math modeling or computer programming experience, ideally in Matlab, Python, or R.

For this project we are seeking people with the following specialties.

Biology/biochemistry: General knowledge of cell regulatory signalling behavior and cancer cell biology. In particular, we are seeking someone who is curious about and willing to dive into the complicated task of translating known biology (signalling pathways, metabolic pathways, genomic information) into computationally usable formats.

Machine learning/optimization: Strong mathematics. Ideally candidates are also familiar with machine learning algorithms including support vector machines (including familiarity with kernels) and random forests, but a strong desire to learn goes a long way.

Genomics/genetics: The genomics candidate should be familiar with various publicly accessible sources for obtaining and packaging up a wide variety of cell-line specific information including gene expression, copy number, mutations, methylation, proteomics. The candidate should also be well-versed in biology in order to assist with transferring these various information streams into a representation suitable for mathematical prediction/machine learning.

Computational pharmacology: Candidates interested in drug repurposing are encouraged to contact David Craft as well.

These positions are unpaid internships. They can begin ASAP and the duration is 6 months, which can be extended if all parties agree.

Please email Dr. Craft a statement of interest and background, as well as a resume or CV.


VMAT (David Craft, This email address is being protected from spambots. You need JavaScript enabled to view it.)

VMAT (volumetric modulated arc therapy) is a radiation technique that involves the radiation beam irradiating a patient continuously as the beam rotates. The beam is shielded dynamically by multi-leaf collimator (MLC) leaves. The leaf trajectory problem, which is the heart of the VMAT optimization problem, is known to be highly non-convex and large-scale. Our group recently devised and implemented a formulation for computing the optimal leaf trajectory problem for VMAT planning, but we now seek to improve the solution time of that approach through parallel processing, improved starting guesses, and other yet-to-be-determined custom heuristics and constraints.


Cancer treatment as an optimal stopping problem (Thomas Bortfeld, This email address is being protected from spambots. You need JavaScript enabled to view it.)

In this project we will consider the treatment of cancer patients with radiation. OR has made a profound impact on the way we treat patients with radiotherapy today, through the development of optimized “inverse” planning and intensity modulated radiation therapy (IMRT). More recently we have considered the optimization of radiation dose delivery over time, the so-called dose fractionation problem. In all those cases it has been assumed that the total radiation dose is fixed, as prescribed by the physician. Here we will lay the theoretical foundation (from an OR perspective) of the question of how much dose to give or how many treatment fractions to deliver, within the personalized therapy paradigm. We will consider the concrete example of hepatocellular carcinoma (HCC). During the treatment of HCC patients we assess the  Child-Turcotte-Pugh (CTP) score, which has the potential to serve as a prognostic factor to determine the outcome for the patient. In our modeling studies we will vary the dose per fraction or the number of fractions to optimize the expected outcome given the day-to-day changes measured in terms of the CPT and related factors such as blood biomarkers. We will put particular emphasis on the uncertainty of the measured parameters and their correlation with outcome, i.e., the robustness of the solution.  


Metastasis (David Craft, This email address is being protected from spambots. You need JavaScript enabled to view it.)

The vast majority of cancer patients who die from their disease die due to the spread of cancer to other areas in their body, a process called metastasis. Managing the metastatic state of disease is currently done without a formal framework and thus is subject to improvement. This project will involve understanding the current patient management strategies being used, and then will proceed to define objectives/goals of a management strategy. With those as preliminaries, the project will involve building a stochastic model of metastasis which will be informed by patient-specific information which may include genomic information in additional to more standard clinical disease staging indicators. The end result will be a model that serves as a framework for personalized management of metastatic cancer.