Week 4: Mathematical Modeling and Montreal

So I missed a few days of the Immersion program teaching for a Math Camp in Montreal. For the summer camp, I was preparing a fun talk that discusses some ways that math can help in the clinical settings. While preparing this talk, I figured there was no better way than asking the immersion clinicians for ideas that I can talk about. So here it is:

As engineers, we often use mathematics as a set of tools for solving problems. From fluid dynamic models of blood flow, to certain clinical data analysis, there are numerous ways to use math in clinical settings. One topic that caught my attention, and fascinated me was the problem of how organ transplants are optimized at the local, regional, and national levels. There is an increasing trend of government funding for an efficient network called the Organ Procurement and Transplantation Network (OPTN). I've seen an analogous problem, (about the renal transplant network) last year in a mathematical modeling contest, and thought this would be a great problem to think about and ask around.
The topic of establishing an effective network is a difficult one, because of the many factors that must be incorporated in developing this model. As there are more organs sought after than there are available, there would usually be a significant waiting list for patients who need a new organ. One could try making a population dynamics model (using a system of ordinary differential equations) to get a holistic idea of how the waiting list behaves over the long course, but many indications suggest that we are all moving more towards larger and larger waiting lists in the future for almost all organs. Supply simply does not meet the demand.

One novel approach for resolving this situation was looking at donor-patient pairs. It is often true that exists a donor who is more than willing to donate an organ to a specific patient (which made sense in the case of a kidney), but the donor's kidneys are not compatible with the patient. If this is the case, it would make sense to establish a two-way exchange, so the two donors would trade their kidneys.

As a mathematician, one would like to generalize into establishing an n-way exchange, and finding a mathematically elegant solution that solves this optimization problem. However, from a clinical perspective, there are additional factors that need to be considered before we consider a similar exchange. First, suppose we establish an n-way exchange, but the chain breaks (eg. extraction fails) at some point. If this happens, what are the repercussions of such failure to the whole chain? One patient will not receive a sought after kidney due to the failure, while its donor, whose kidney is somewhat like a bargaining chip for acquiring his or her patient's new kidney, may break off; would this result in the entire chain of surgeries to fall apart? If so, will that mean that the all n transplants must happen simultaneously? Second is the feasibility of such cyclic surgeries; after all, these n-way exchanges require a lot of clinical manpower. Do most facilities have such capabilities? While it may be possible to model these intricacies using mathematics, it still won't address all the questions that clinicians may have.

Through summer immersion, I've learned that to address these problems properly, it would require more than mathematical problem-solvers developing models; a collaboration with clinical experts who work hands-on with these issues is a must. It is interesting to see where these considerations may lead to: NYP-Columbia Hospital was successful in having a 3-way exchange for the renal transplant recently in 2004, and this was a huge step forward.

Last diverse week! Gotta get my project going from now on.

I have had it with surgeries. This week I attended an arm reconstruction in the plastic surgery unit, which was great, but I think it's gonna be my last one. Nothing is wrong with it; it's just interesting for the first 15 minutes and then after that, it's just a lot of tissues with some blood being push around for a long time. I'm much more interested in trying to figure out what's wrong with the patient and what would be the best treatments. I'd be happy with just hearing about what will be done in a surgery in order to fix the problem rather than watch for 3 hours and try to figure out what's going on. I think the thing I learn the most when observing a surgery is about anesthesia. It seems so much easier in human. I'm not sure if it's because my mouse is way smaller than a person, so it's harder to maintain appropriate level of anesthesia; or may be the anesthesiologists are just a thousand times better with human than I am with mice.

Anyway, a saw or something fell on this patient's arm and almost cut off his wrist since he works as a construction worker. (And don't you dare tell me that this is too much identifiable information on a public blog. There are thousands of young male construction workers in NYC. I'll give you 50 bucks if you can actually identify this patient! --except those of you who saw the surgery, of course) To fix this, Dr. Spector and the team had to reconnect the nerve bundle. The problem is, the nerve tissue was too short to be sew back together, so they used endothelium flap to connect both nerve endings. My thought throughout this whole process was on a talk I attended at one Biomedical Engineering Society conference. One group showed that axon of a neuron can be stimulated to grow up to 15 cm during a period of several weeks if a constant, small PHYSICAL force is applied. I can't help but keep thinking that if the surgeons can preserve the nerve tissues while stretching them for a few weeks, the neurons will grow longer. They can then connect the endings without using the endothelium which doesn't conduct as well as nervous tissues. It seems like it'd work...

Hematology clinics this week was extra cool because I suggested radiation therapy for a patient with uncontrollable Chronic Myeloid Leukemia and Dr. Silver actually took it. I might start asking for a commission if he takes a few more of my wild suggestions :) The patient had very high white count among a whole bunch of other elevated components of the blood. He feels tired and sick and had insomnia and etc. due to his condition and drugs side effects. I'm not sure why, but Dr. Silver never prescribe radiation therapy. He always uses chemo drugs only.

My favorite case this week was with Dr. Prince. It was the first time I observed a physician making a diagnosis by looking at an MRI. An MRI scan of a 74 year old lady showed that she has a stenosis on the artery that goes to her left kidney. She has hypertension because of this incomplete blockage, and her right kidney is dying due to this pressure. However, she feels fine. There's no symptoms whatsoever. Dr. Prince said the location of the stenosis is an easy location to put a stent in, however, there are still risks. The dilemma is that she feels fine. Should she risk putting a stent to fix the arterial blockage? And if she doesn't have this operation, her right kidney will completely stop functioning eventually. If she opens up the blockage, then the hypertension could still remain and that will kill the currently good left kidney. I find the decision making process in order to balance the risks and the advantages more challenging and fun.

A rough day...

Today I think reality set in. I had pretty much a normal day, but at the same time a very rough day. I started off in surgery with Dr. Scherr as normal watching a robotic cystectomy with an Indiana pouch and then left to do NICU rounds with Dr. Frayer. The difficulty began when I walked into the NICU and a group of doctors and nurses were looking at a head sonogram. First of all, the subtleties they could observe was amazing, but the prognosis was also very challenging. As we later made our rounds, I realized this was a baby I had learned the name of just yesterday. And as the doctors and nurses discussed how they would present the situation to the parents, I realized that this tiny baby will have a very rough ride in the days to come. After rounds I returned to Dr. Scherr's surgery which was going very well. The surgeons ran into some difficulties near the end as the patient had previously received radiation and some of the tissue was very fragile. Just as they were finishing though, Dr. Scherr received a phone message from his secretary. A patient from just days before, having received a robotic cystectomy and recovered very well, had fainted in his hotel, was rushed to the ER and had passed away. Dr. Scherr then left the residents to finish closing as he went to find the wife of his patient in the ER and learn what had happened.

Over the past few days I've finally had the chance to do rounds with the residents. While they didn't understand why I would do this, it was very valuable to me to be able to see patients recover. What I didn't expect was the impact of learning the patient names (which I also did in the NICU to be able to keep track of the babies). I had previously tried to avoid writing down names in order to maintain patient privacy, but at this point I feel like I was somehow dehumanizing them by not noting their names. Now I try to keep track because although the two instances mentioned above are very difficult, they're also very real. Today definitely brought me out of the solely science aspect of medicine and into the humanity aspect of medicine.