Professor Malcolm Levitt is Head of Magnetic Resonance at the University of Southampton and a leader in the field of magnetic resonance research. In the early 2000s, he began programming SpinDynamica—a set of *Mathematica* packages that run spin dynamical calculations—to explore magnetic resonance concepts and develop experiments.

SpinDynamica is an open-source package that Professor Levitt continues to work on as a hobby in his spare time, but the SpinDynamica community also contributes add-ons to bring additional functionality to researchers.

Professor Levitt graciously agreed to answer a few of our questions about his work, *Mathematica*, and SpinDynamica. He’s hopeful that as word spreads, others will submit add-ons that enhance the core functionality of SpinDynamica.

**What is your history in the field of magnetic resonance?**

I’ve been researching in magnetic resonance since I was an undergraduate project student in Oxford in the late 1970s. I went on to do a PhD in Oxford, researching in nuclear magnetic resonance (NMR) with Ray Freeman. After that, I went off on a long sequence of postdoctoral positions. I worked with Richard Ernst in Zürich, who later won the Nobel Prize for his work on NMR.

I researched at MIT for about five years, and then became a professor in Stockholm, Sweden, before moving back to the UK in 2001. I now lead a magnetic resonance section at the University of Southampton. Most of my research has involved developing the theory and technology of NMR. It’s an amazingly rich field, since NMR is time-dependent quantum mechanics in action, and allows an instant coupling between a theoretical idea, a numerical simulation, and a real experiment.

There are now many thousands of distinct NMR experiments, involving different sequences of radio frequency pulses and switched magnetic fields, providing information on everything from biomolecular structure to cancer diagnosis to quantum computing. It really is a staggeringly versatile field of research, and I feel very lucky to have stumbled into it and to have made my career in it.

**When did you begin working with Mathematica? **

I started using *Mathematica* seriously for magnetic resonance research in the 1990s in Stockholm. During my PhD and in Zürich, I had written a lot of low-level code for controlling an NMR spectrometer, as well as graphical FORTRAN simulations of NMR experiments. Later on, while I was at MIT, I developed a lot of FORTRAN computer code for simulating magnetic resonance experiments, which I tried to make as general as possible. However, I always recognized the limitations and inelegance of the language.

When I first encountered *Mathematica* I remember a sense of recognition like, “Wow, this is exactly the computer language I would have invented myself if I had known how.” However I do remember at that time *Mathematica* seemed slow in execution and there would be times of frustration. Nevertheless I stuck with it. Happily, the progress of hardware and continued development of *Mathematica* made my commitment worthwhile.

**What can you tell us about SpinDynamica and how you created it?**

I started to use *Mathematica* seriously for NMR research in Stockholm, partly in combination with a book that I was writing (*Spin Dynamics*), for which I wanted to generate informative graphics and check the equations. At that time, I did experiment with creating a set of modules for numerical simulations of NMR experiments, as well as generating analytical results, but I did not develop this very far.

Several other numerical simulation packages for NMR came out. Although they were numerically fast for specific classes of problems, I still felt that they were not as general and as elegant as I would like. Furthermore, our group was getting into experiments that required certain types of numerical simulation that were not catered for. So at some point in the early 2000s I set about seriously developing general packages for both symbolic and numerical calculations of magnetic resonance, within the *Mathematica* environment.

**How do you use SpinDynamica in your research?**

*Mathematica* in general, and SpinDynamica in particular, have become completely central to how I develop and test theoretical ideas. So it’s not as if I develop an idea and then test it with SpinDynamica—I actually use SpinDynamica as a tool to develop the idea in the first place. It’s a bit hard to explain, but it works for me. There’s something about *Mathematica* that seems to match perfectly the way I think and create.

**Is there an interesting example or discovery you’ve come across while working with Mathematica and SpinDynamica?**

A central topic of research in our group concerns something called long-lived spin states. These are certain quantum states of coupled magnetic nuclei that are very weakly coupled to the environment. They may be used for storing quantum information in nuclear spin systems for long times. (We have demonstrated over 30 minutes, which is an incredibly long time for a quantum effect in a room-temperature liquid.)

In the jargon of magnetic resonance, the equilibration of the nuclear quantum system with the environment is called relaxation. So these special nuclear spin states have very slow relaxation. It is a surprising fact, but true, that although the relaxation theory of NMR has been extensively developed with thousands of research papers since the 1960s and several Nobel prizes along the way, the existence of these states had been overlooked.

It was only when the symmetry properties of the relaxation were examined with *Mathematica* (using a precursor of SpinDynamica) that the presence of such states was predicted, and then demonstrated experimentally by our group in 2004. Our group is intensively researching the theory of these states and their exploitation in practical NMR experiments and, hopefully, in clinical MRI as well. Amongst other things, we are working with collaborators to develop agents that use long-lived states to detect cancer.

**What impact do you think SpinDynamica could have on future magnetic resonance research?**

That is hard to predict. There are several simulation packages in the community, many of which require less user intelligence, and which have a much faster execution for specific problems, than SpinDynamica. SpinDynamica is immensely powerful, but it does require that users have a good theoretical understanding in order to use it.

That weakness could be addressed by including additional packages for simulating common experimental situations without major theoretical understanding. The problem is that, at the moment, SpinDynamica remains a hobby project that is developed almost exclusively by me in my spare time. So although it is a superb tool for our particular branch of research, which demands a high theoretical level, there are many aspects that are rather undeveloped, including some important functionality that I have simply never had time to develop.

Nevertheless, I think the core functionality of SpinDynamica is powerful and stable, and I hope that the community will take it and build on it. That is slowly starting to happen. I have taught several graduate-level courses using SpinDynamica to explain the quantum-mechanical concepts of magnetic resonance, so there is take-up by a small but growing group of scientists. I think the impact will become much greater when I find time to write up a proper scientific paper on the architecture and functionality of SpinDynamica. Unfortunately my schedule makes that unlikely to happen soon.