Therapy by Numbers

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Dr. Billie Sandak uses a computer language developed at the Weizmann Institute to standardize the therapy process

Mathematical computations, equations and computer languages are not the first thing one thinks of when looking for ways to improve therapies that treat patients with drawing, painting, music or dance. But Dr. Billie Sandak, in the research group of Prof. David Harel of the Weizmann Institute's Computer Science and Applied Mathematics Department uses these in developing a computerized research method that may give both researchers and therapists a quantitative tool for measuring the processes that take place in arts therapy and creation.

Dr. Billie Sandak and Prof. David Harel

Sandak earned her Master’s degree in computer science and mathematics from the Weizmann Institute in 1991. Through her work in developing computerized mathematical models for a pathogen-induced immune system response, she became acquainted with a visual computer language that had been invented by Prof. David Harel in 1984, called "Statecharts".

After being awarded a PhD in computer science from Tel Aviv University, in computational and structural biology, Sandak carried out postdoctoral research at the Weizmann Institute, developing methods for accelerating scientific computations. Over the years she has worked in international high-tech firms, earned an MBA and led a self-initiative in the pharmaceutical industry. Along the way, she also developed a love for the arts, which in turn exposed her to the world of arts therapies – treating people through drawing and painting, music, dance and movement, etc.
Relevant facts

But she also, as a scientist, found that this area leaves a lot to be desired. Art therapists, psychologists, social workers, researchers and other experts do not adequately understand the mechanisms underlying the treatment. And yet, there is no escaping the fact that many patients report improvements in their lives – for example, less pain, stress, depression, shortness of breath or tiredness, and better social interaction.
Visualization of art dynamics. A tracking graph of color and tool choices, erasures, time durations, their use and location on the drawing page, the pressure exerted on the tools and drawing stroke gradient

Sandak talked with therapists, researchers and related experts, and learned that the human observer finds it difficult to grasp, and thus to fully document and analyze all of the many processes that take place in the therapy room. The therapists’ documentation is usually written, whereas the treatments are visual, musical, auditory and physical; and the interaction between patient and therapist takes place primarily on these levels, as well.  

Relevant facts for example, might include whether the lines the patients drew were thick or thin. What colors they chose. Whether they prefer pencils or paintbrushes. What musical instruments they picked up. Whether the sound they played was soft or loud, high or low.  How much pressure they exerted on the drawing tool or the eraser. How much of the page they covered with drawing, and how much was left blank.

Sandak decided to create a rigorous method to quantify and analyze this kind of dynamic information. Her proficiency with Statecharts brought her back to the Weizmann Institute of Science and to Harel’s research group.

Statecharts is a language used to visually describe the behavior of large reactive systems with many components – for example, systems that exist in airplanes, vehicles and smartphones, as well as biological and social systems and networks. The Statecharts method creates a collection of the states and events that together depict all the possible interactions between the components in a system. In this way, it can cope with a system that has an enormous number of possible outcomes or intermediate steps, and its models are presented visually in a way that is intuitively clear yet mathematically sound. In biology, for example, it is used to model how a cell will react – not just to a particular substance, but to that substance within the context of the other cells it “talks to,” its environment and other substances that affect its function.



Sandak and Harel, working together with Profs. Orly Sarid and Ephrat Huss of the Ben-Gurion University of the Negev, first defined specific states and events that occur in the therapy room.  For art therapy, the Statecharts model they developed included tracking the characteristics of the brushstroke or line, tool and color choices, the pressure exerted on the drawing tools, erasures, speed of drawing, amount of page covered and more.

The scientists then conducted an experiment with a dozen volunteer subjects. Every participant had four drawing tasks to carry out, which were not limited in time: To choose one color out of ten and draw lines using all six available drawing tools; to artistically express a positive feeling; to draw an image of a negative feeling;  to draw a house with a tree and person. In the latter three tasks, the participants could use the colors and tools of their choice. The researchers divided the subjects into age and gender groups for analysis.
New insights into the human mind

The analysis showed that the women participants drew twice as fast as the men; that men used the color blue and lead pencil about three times longer than women did; that men used more types of drawing tools than women; that the older participants erased more than younger ones, while the latter used more colors.

The method and findings, which appeared in PLoS ONE, may with more research provide researchers and therapists with an empirical tool to test or generate hypotheses and to develop ways to track the progress of patients and improve treatments. These may also ultimately lead to new insights into the human mind. In addition to drawing and painting, the method can be adapted to other forms of arts therapies – for example music or dance therapy.  
Prof. David Harel’s research is supported by the Benoziyo Fund for the Advancement of Science; the Braginsky Center for the Interface between Science and Humanities; the Willner Family Leadership Institute for the Weizmann Institute of Science; the J&R Center for Scientific Research; the Philip M. Klutznick Fund for Research; Erica A. Drake and Robert Drake, Scarsdale, NY; and the wstate of Dora Joachimowicz. Prof. Harel is the incumbent of the William Sussman Professorial Chair of Mathematics.