Patient care in the ICU in terms of vectors and topological spaces
Biomedical Informatics, Medicine
A few weeks ago, [Timothy G. Buchman](http://www.gsres.wustl.edu/Residency/Facultycv.asp?Drid=97&CVType=F) gave a talk at the [Columbia <acronym title=”Department of Biomedical Informatics”>DBMI</acronym>](http://www.dbmi.columbia.edu/) weekly research seminar. During the QA session, someone asked why patients in intensive care units (ICUs) were given such “extreme” treatments, often causing them to develop new health problems and complications, keeping them in the hospital. He replied with this wonderful mathematical metaphor about patient care.
You are a point in an n-dimensional space. Each dimension is some vital sign or homeostatic attribute, e.g. blood pressure, blood glucose, temperature, etc. Homeostasis is defined a polytope in that space. As you do the various things of life, your point moves within the space defined by that polytope. For example, when you eat, your blood sugar goes up, and the point moves along in the blood sugar dimension; when you take a cold shower, your body temperature is reduced, and you move along in that dimension. Young people have a large space inside their homeostatic polytope
When you leave this homeostatic polytope, you're considered “sick.” If you travel to far from it, you die.
People who enter the <acronym title=”Intensive Care Unit”>ICU</acronym> have points that are moving away from their homeostatic polytope. Their movement away can be represented as a vector, representing how quickly their condition is deteriorating.
Treatments in the ICU represent vectors that try to point you back towards your homeostatic polytope.
