David Craft, PhD

Assistant Professor, Harvard Medical School and MGH
Head of the Optimization and Systems Biology Lab
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Associate Member, Broad Institute

Education and Degrees

B.Sc.: Brown University, Mechanical Engineering, 1996
Ph.D.: Massachusetts Institute of Technology, Operations Research, 2004

Areas of Interest

Mathematical modeling, systems biology, genomics, immunology, biological network modeling, radiation for cancer control, machine learning (kernelized support vector machines, random forest, neural networks).

Multi-criteria optimization in radiation therapy. Convex optimization, mixed integer programming, global optimization.

Mathematics and statistics.

Research statement 

My current focus is on the development of machine learning approaches for personalized cancer treatment. The main research questions are: what is the value of prior knowledge in this domain and how can we best incorporate such expert knowledge. We have recently published two papers that clearly demonstrate that for complex systems it is highly useful to incorporate expert knowledge when using machine learning to predict the system behaviors (see here [supplementary info] and here). 

We are pursuing cell line drug and radiation sensitivity datasets as a critical step towards the eventual development of a clinical personalized drug selection tool for cancer. This research is ongoing but please reach out to me at [reversed] broadinstitute.org [at] dcraft to discuss directions, pitfalls, new ideas, etc. Specifically, we built a drug recommendation system for cell lines: for a new sample (a patient or a cell line), can we recommend a good drug and dose? See our pre-print article, Dr.S (drug recommendation system) here. See also the work that led to this: Georgios Patoulidis' masters thesis.

In the field of cancer immunology, I am working with some other folks at the Broad on the MHC class 1 peptide binding prediction problem. We are building a software framework called PACE (peptide algorithm comparison environment) which will allow researchers to cleanly compare their machine learning (or molecular docking) approaches to this problem. 

In the world of radiation therapy, I consider VMAT still an unsolved problem. It is highly non-convex, and yet there are many convex aspects to the problem. My group is working to tame those non convexities by smart heuristics. Here is a recent paper.

In the summer of 2019, Bella Craft, a high school student, interned with me. One of her projects became this essay on cancer.


Probabilistic Definition of the Clinical Target Volume - Implications for Tumor Control Probability Modeling and Optimization, PMB, 2020.

A Drug Recommendation System (Dr.S) for cancer cell lines, arXiv, 2020.

Simulation-assisted machine learning [supplementary info], Bioinformatics, 2019.

Improving VMAT delivery efficiency by optimizing the dynamic collimator trajectory, Medical Physics, 2019.

Dynamic fluence map sequencing using piecewise linear leaf position functions, BPEX, 2019.

Impact of setup and range uncertainties on TCP and NTCP following VMAT or IMPT of oropharyngeal cancer patients, PMB, 2019.

The clinical target distribution: a probabilistic alternative to the clinical target volume, PMB, 2018

Multi-criteria optimization and decision-making in radiotherapy, EJOR, 2018.

The value of prior knowledge in machine learning of complex network systems, Bioinformatics, 2017. Datasets for download (including README instructions) and Matlab Boolean Network Creation Simulation package: RaBooNet

PICS: Pathway Informed Classification System for cancer analysis using gene expression data Cancer Informatics, 2016.

The price of target dose uniformity, International Journal of Biology, Physics, and Medicine, 2016.

Craft and Balvert VMAT papers: Fast approximate delivery of fluence maps: the single map case and the VMAT case. 2016. We rolled this paper into one to publish it: Fast approximate delivery of fluence maps for IMRT and VMAT. 2017

Within the next five years, most radiotherapy treatment schedules will be designed using spatiotemporal optimization, point/counterpoint. Medical Physics, 2016. 

Volumetric-modulated arc therapy using multicriteria optimization for body and extremity sarcoma, M. Young et al. JACMP 2016.

Multi-criteria optimization achieves superior normal tissue sparing in a planning study of intensity-modulated radiation therapy for RTOG 1308-eligible non-small cell lung cancer patients, Kamran et al, Radiotherapy and Oncology, 2016.

Shared data for intensity modulated radiation therapy (IMRT) optimization research: the CORT dataset GigaScience, 2015.

Optimization approaches to volumetric modulated arc therapy planning J Unkelbach, T Bortfeld, D Craft, M Alber, M Bangert… - Medical physics, 2015

A circular matrix-merging algorithm with application in volumetric intensity-modulated Arc therapy DZ Chen, D Craft, L Yang - Theoretical Computer Science, 2015

Three-dimensional conformal planning with low-segment multicriteria intensity modulated radiation therapy optimization, Kahn, Craft.  GigaScience, 2015.

Optimization approaches to volumetric modulated arc therapy planningUnkelbach, Bortfeld, Craft, et al, Med Phys, 2015.

Plan averaging for multicriteria navigation of sliding window IMRT and VMAT, Med Phys, 2014.

Multi-criteria optimization methods in radiation therapy planning: a review of technologies and directions. Springer, submitted.

Guaranteed Epsilon-Optimal Solutions with the Minimum Number of Beams for Stereotactic Body Radiation Therapy, Yarmand, Winey, Craft. PMB (2013)

A hybrid approach to beam angle optimization in intensity-modulated radiation therapy  Bertsimas, Cacchiani, Craft, Nohadani. Computers and Operations Research (2013).

Maximizing dosimetric benefits of IMRT in the treatment of localized prostate cancer through multicriteria optimization planning, Medical Dosimetry, 2013.

Deliverable navigation for multicriteria step and shoot IMRT treatment planning, Physics in Medicine and Biology, 2013.

The dependence of optimal fractionation schemes on the spatial dose distribution, Physics in Medicine and Biology, 2013.

Exploring Trade-offs between VMAT Treatment Quality and Delivery Efficiency, Salari et al, Physics in Medicine and Biology, 2012.

Optimal partial-arcs in VMAT treatment planning,Jeremiah Wala, Ehsan Salari, Wei Chen and David Craft, Physics in Medicine and Biology, 2012.

Including robustness in multi-criteria optimization for intensity-modulated proton therapy, Wei Chen, Jan Unkelbach, Alexei Trofimov, Thomas Madden, Hanne Kooy, Thomas Bortfeld and David Craft, 2012 Phys. Med. Biol. 57.

Multicriteria VMAT optimization, Medical Physics, 2012 

Improved planning time and plan quality through multicriteria optimization for intensity-modulated radiotherapy.International Journal of Radiation Oncology * Biology * Physics, 2011

A fast optimization algorithm for multicriteria intensity modulated proton therapy planning. Chen, Herman, Craft, Madden, Zhang, Kooy. Medical Physics, 2010; 37(9).

Simultaneous navigation of multiple Pareto surfaces, with an application to multicriteria IMRT planning with multiple beam angle configurations. Medical Physics 2010;37(2).

Calculating and Controlling the Error of Discrete Representations of Pareto Surfaces in Convex Multi-Criteria Optimization. Physica Medica. 2010.

Multicriteria Optimization in IMRT Treatment Planning For Locally Advanced Cancer of the Pancreatic Head. International Journal of Radiation Oncology * Biology * Physics, 2008;72(4):1208-1214.

Evaluating Target Cold Spots By the Use of Tail EUDs. International Journal of Radiation Oncology * Biology * Physics, 2008;71:880-889.

How Many Plan Are Needed in an IMRT Multi-Objective Plan Database. Physics in Medicine and Biology. 2008;53:2785-2796.

An approach for practical multiobjective IMRT treatment planning, Int J Radiat Oncol Biol Phys. 2007;69(5):1600-1607

The tradeoff between treatment plan quality and intensity field complexity in IMRT, Red Journal, volume 67 number 5, April 2007

Local beam angle optimization with linear programming and gradient search. Phys. Med. Biol. -- March 2007 -- Vol. 52, pp. N127-N135.

Dose-volume objectives in multi-criteria optimization (Halabi et al., Phys. Med. Biol. -- August, 2006 -- Volume 51, pp. 3809-3818)

Approximating convex Pareto surfaces in multiobjective radiotherapy planning(Medical Physics -- September 2006 -- Volume 33, Issue 9, pp. 3399-3407)

Exploration of tradeoffs in intensity-modulated radiotherapy (2005, Physics in Medicine and Biology)

Maximizing Operating Room and Recovery Room Capacity in an Era of Constrained Resources, Arch Surg. 2006;141:389-395.

Surgeon Profiling: A Key to Optimum Operating Room Use, Arch Surg. 2007;142:365-370

Ph.D. Thesis: Local energy management through mathematical modeling and optimization

Analyzing Bioterror Response Logistics: The Case of Anthrax (May 2005, Management Science, Volume 51, Number 5)

Analyzing bioterror response logistics: The case of smallpox (2003, Mathematical Biosciences, Volume 185 Issue 1)

Emergency response to a smallpox attack: The case for mass vaccination (2002, Proceedings of the National Academy of Sciences)          - Work discussed in the New York Times, July 9, 2002

Emergency Response to an Anthrax Attack (2003, Proceedings of the National Academy of Sciences)

A Mathematical Model of the Impact of Novel Treatments on the A-Beta Burden in the Alzheimer's Brain, CSF and Plasma (2001, Bulletin of Mathematical Biology)

Bower, A.F. and Craft, D. (1998) Analysis of failure mechanisms in the interconnect lines of microelectronic circuits. Fatigue & Fracture of Engineering Materials & Structures 21 611-630


Some of Infinity: peaks in the landscape of mathematics, (Center of Mathematics, 2017).

Quotes from the back of the book:

“Some of Infinity is a spirited and fun jaunt through the math you don’t learn in school (and some that you do.)  This is math the way a mathematician sees it: not as drudgery but as a form of play.”

Jordan Ellenberg (author of How Not to Be Wrong, Professor of Mathematics, University of Wisconsin)

"From fractals to probability, Craft takes complex topics usually relegated to academic circles and makes them fun and accessible for all.  More than just providing simple understanding, he inspires readers to play with logic and numbers. If grade school math were taught more like this, students would have less anxiety and we'd be a more numerate society."

Aaron Santos (author of How Many Licks?: Or, How to Estimate Damn Near Anything, Assistant Professor of Physics, Simpson College)


Urban Foraging, Finding and eating wild plants in the city, Service Berry Press, 2011.


Hammer and Tongs, 2004

Return To Their Natural Coast, 2012

Furniture Music, 2016


My foraging tours schedule at foragelive.com

Located in: Past Members