With recent massive increases in both the amount of medical scanning data and the ability to analyze said data, a lot of new possibilities for biomedical data analysis are emerging. A really simple but effective way of analyzing medical data is just segmenting the shape of some organ or body part (the heart, the brain, the hand, etc.) and producing a statistical model of its shape. Why is that interesting? Well, here are some uses:
- Image segmentation. It’s hard work, and having a statistical model of what it is you’re trying to segment can be really useful.
- Being able to correlate, say, the shape of an organ to some biophysically relevant parameter (metabolism, age, etc.)
- Developing patient-specific models for personalized medicine.
- Obtaining clues about organ development. This is exciting, since you can then correlate those clues with data from genetics to figure out how various genes work in development and disease.
This type of shape analysis isn’t new; there’s an excellent review by Tobias Heimann (2009) which went over the state of the art at the time, and since then the field has been only expanding. See Coote’s 2014 paper for a more recent-ish review.
My work lately has been focused on building a statistical model for an organ with a much more complex shape than e.g. the liver or the heart. I can’t reveal the details yet (we have 2-3 papers in the process of review right now) but I can talk about a recent paper that is pretty interesting and relevant to anyone who wants to get into this field: Alessandra Scarton (2016). In it, they study the problem of generating a parametric foot model.
Foot models with PCA
Lower limbs are a prime target for statistical modeling, as they are fairly complex in terms of shape and thus time-consuming to segment individually. There is the potential for better time-efficiency by building a statistical model for the general population and then tweaking the model to represent the anatomy of an individual patient. Once a personal patient-specific model has been constructed, you can then use computational simulation (using, e.g. finite element analysis) to model that patient’s motor ability.
In the 2016 paper, they focused on the first metatarsal bone; this is the bone in the foot just behind the big toe. The reason being that the area underneath this bone is at very high relative risk for foot ulcers. They also analyzed overall external foot shape (excluding toes).
The first major step in doing shape analysis is usually aligning all the shapes to some common reference frame. This isn’t always an easy problem! If you want to align, say, mouth shapes, well you can align the subject in a forward-facing, upright position. If you want to align, for example, shapes of boats, you can orient the boats so that their keels all face the same direction and the boats are floating level. In these cases, there are well-defined landmarks which you can align the shapes to. But sometimes, shapes lack clear landmarks. For example, how do you align white blood cell shapes? (Incidentally, shape alignment for cells was a major focus of my thesis). The answer: you can’t. Well, not deterministially, anyway. A lot of the time you have to settle for probabilistic alignment — generate a set of candidate alignments, and try them all. Sometimes you can figure out the ‘correct’ alignment after trying them all out. Other times there’s no well-defined way to figure out what is the correct alignment, so you really just have to take all the alignments into consideration and weigh them according to their probabilities.
Anyhow, in this paper, they use ICP for shape alignment. ICP is a relatively simple method that’s been used pretty widely. There’s matlab and OpenCV tools for doing it. It’s a fairly old method, though, and more recent methods like CPD out-perform it. However, depending on the application, it may be good enough.
After using ICP to align the foot shapes, they use a k-NN algorithm to match the number of vertices in the target shape to the reference shape. They then do PCA on the resulting vertex coordinates.
After this, they then display the effect of varying each of the resulting PCA modes while keeping others constant. The modes with largest variabilty were (expectedly) related to the bone thickness and length. Other modes were related to curvature of the bones. They also did within-group PCA, analyzing the modes within diabetic subjects and healthy subjects separately.
All in all, this is a very simple yet illuminating view into what even simple statistical analyses can reveal about shapes. Historically, these kinds of judgements all had to be made by human expertise. Nowadays we can quantify and measure them automatically.