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In today’s world, we’ve all unfortunately been touched by cancer in one way or another.  We may have stood beside a loved one as they battled the disease, or we may have experienced it first-hand.  Rick at First Dayton Cyberknife encounters cancer patients on a daily basis as he assists in their treatment.  I’m thankful for folks like him who use their math skills effectively to help others.

Can you explain what you do for a living?

I am a certified medical dosimetrist at First Dayton Cyberknife. I work in radiation therapy which is used to treat people who have cancer. I make sure the radiation kills the cancer cells without harming the patient.

The medical dosimetrist is responsible for designing a treatment plan and carrying out calculations with mathematical accuracy for the delivery of radiation treatment based on the oncologist’s prescribed course of therapy. This treatment plan takes into consideration tumor pathology, tumor volume, and inherent dose-limiting structures surrounding the tumor. The treatment plan and radiation field-placement techniques are constructed utilizing sophisticated computer equipment and technology. The medical dosimetrist, along with the radiation oncologist and medical physicist, will work to construct a treatment plan that will meet the prescription written by the oncologist, ensuring that the patient will not lose important healthy organ function and that the radiation delivered will not affect healthy surrounding tissue. These treatment plans not only include the use of radiation but also, in many cases, involve the use of radioactive elements during interstitial brachytherapy procedures. Once the treatment plan is complete, the medical dosimetrist will work closely with the radiation therapists in the implementation of the prescribed plan.

When do you use basic math in your job?

My whole job is math related. I wouldn’t be able to do my job without math skills. Most of my job pertains to the physical properties of radiation and its interactions with matter. There are calculations depending on energy, energy type (photon, electron, gamma ray), size of the treatment field etc. Most of these calculations are done using a treatment planning system (TPS). We use Eclipse, which is from a company called Varian. We also use a Cyberknife, which uses a software called MultiPlan.

Do you use any technology to help with this math?

Most of the time I use specialized software for treatment planning but not always. Some plans have to be hand calculated.  

Sometimes I use a hand calculation to basically determine how long the machine needs to stay on to deliver a certain dose to a certain depth. For example, the radiation oncologist will prescribe 2400 cGy (centigray is a unit of absorbed dose) in 10 treatments (240 cGy per treatment) to a depth of 80% or sometimes he will say 2 centimeterss. I will use a simple formula that we call a hand calc, 240 

80% • 1.002 =299cGy
(where 1.002 is the output factor of field and energy)

1 cGy=1 monitor unit on the machine so the machine would be set to 299 mu’s per treatment for ten treatments for 100% coverage of radiation at the 80% isodose line. This is confusing as heck so I won’t get any deeper with this because I will just go on and on and on….

This is a very simple calculation. Most of the time we aren’t this lucky. Actually most of the time everything is calculated with the Treatment Planning System.

How do you think math helps you do your job better?

Math is physics and physics is math, so you can’t have one without the other.

How comfortable with math do you feel?

I feel very comfortable with some math, but with other math I still feel very uncomfortable.

What kind of math did you take in high school?

The highest I took was Algebra II. I barely passed!

Did you have to learn new skills in order to do the math you use in your job?

I have had to learn new calculations for new procedures depending on the type of treatment. Some treatments use a real source of radiation which has different factors. In college, medical physics and radiation physics were totally new to me. I can’t really compare it to normal math class. Lots of formulas, laws and other “math stuff.”

One law that is common is radiation is called the inverse square law: In physics, an inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. That is one of the first things you learn.

Want to know more about using math in the fight against cancer?  Let me know, and I’ll be sure to ask Rick your questions.

No. I do not have cancer. But in April and May and June of this year, I thought I might.

So that’s the answer to the question in my headline. I’ve been taking a break while I deal with the roller coaster of emotions that come with suspicious mammogram and biopsy results and then surgery. First, the story.

In April, I had an ordinary, run-of-the-mill mammogram. I’m what you call a non-compliant patient, and so I’ve only had one other mammogram in my life. Turns out both of these great experiences ended up with biopsies. My first feeling was to be totally pissed off. I’d had a biopsy before, and let me tell you, they are not fun. And since the first one showed nothing, I expected that this would be more of the same — an exceedingly uncomfortable and nerve-wracking experience that showed nothing.

Except it didn’t. The biopsy showed “atypical” cells. This means I had something called Atypical Ductal Hyperplasia or ADH. This is not cancer. These atypical cells cannot even be called precancerous cells. My amazing surgeon explained: Research shows that women with ADH have an increased chance of those atypical cells becoming cancer. Here are the numbers:

  • Women without ADH have about a 5 percent chance of getting breast cancer.
  • Women with ADH have a 20 percent chance of getting breast cancer.
  • And that means women with ADH have four times the chance of getting breast cancer.

For me, those numbers pointed to a very easy decision: to have the area with ADH removed. On July 5, I had a lumpectomy. Then I waited for the pathology results. I waited for 10 days.

Anyone who has gone through something similar knows the special hell these ten days were. I am not a particularly emotional person. And yet, these ten days were downright terrifying. And here’s why.

There was a 20 percent chance that the lumpectomy would reveal cancer. In other words, there was a slight chance that the biopsy missed any cancerous cells that were already there. Of course, that meant I had an 80 percent chance of no cancer at all.

After the surgery, I updated my friends and family. One physician friend emailed me back: “I hope you find some solace in those stats (ie the 80%).” I assured her that I did. (No lie at that point.) And she followed up with this:

“Glad to hear how you’re taking it. You are right about the stats.  They are often very difficult for patients, because if there is a small chance of something, but a patient has it, that patient has 100% chance of having it, right? But we as physicians use stats all the time, especially in the office setting where you don’t have any and every diagnostic test at your fingertips, and with the cost– psychological and financial– to the patient: what is the chance that this patient with this headache and those symptoms has a brain tumor? What are the chances that this person’s chest pain is a heart attack and not indigestion? It is probability, given symptoms, age, and a slew of other factors, in combination with the implications of a given diagnosis.”

These numbers were supposed to ease my mind. Except feelings + stats + time = complete and utter freak out.

By day nine of my waiting period, I was a total wreck. I cried all day long. I wasn’t sure if I was going to be able to sleep. I was nervous as a long-tailed cat in a room full of rocking chairs.

Happy ending: I don’t have cancer. I know that not everyone gets that amazing news, and I am extremely grateful. I am being followed very closely, because my chances of getting breast cancer are still higher than most women’s. And I’m taking tamoxifen for the next five years, which reduces my chances by half. Those aren’t bad stats either.

I never thought that math was the be all end all, but I have often railed against misinterpreting numbers to incite fears and advocated for the use of statistics to ease worry. Still, feelings don’t always play well with math, I’ve found. When a person is worried — scared, even — a pretty percentage may not be comforting. And that’s okay, too. We all do the best we can with what we’ve got.

What’s your story with health and statistics? Has a percentage ever frightened you to the point of distraction or temporary insanity? Share your story here. You are not alone!

Math Appreciation Month has finally come to a close. And I thought I would end with some math that could save your life. This is serious — and I think really interesting — stuff.

If you’re seen a recent “best college degrees” list, you probably wondered two things: Why the heck is Applied Mathematics on the list, and what is it? First off, applied mathematics is not about crunching numbers. Instead, these folks use higher level mathematics — from abstract algebra to differential equations to statistics — to solve a myriad of problems in a myriad of industries. And that, my friends, is why it’s on the list. In industries like energy, cell phone technology and medicine, math modeling and statistical analysis have been applied to solve really big problems.

Math modeling is one branch of this field that has become a very big deal. Let’s say a city planner wants to know how many snow plows to buy so that the city isn’t paralyzed by a winter storm. Modeling this problem using mathematics is one way to address this problem. The way I look at it, math modeling helps us understand things we can’t see — because they’re part of situations that haven’t occurred or are too far away or are too tiny and hidden.

That too tiny and hidden part that is what math modelers are honing in on with medicine. In this field — sometimes called bioinformatics or computational biology — mathematicians help medical professionals address problems that are under the skin. Here are two examples:

Fighting Cancer: Researchers at University of Miami (UM) and University of Heidelberg in Germany have created a math model that will help oncologists predict how a tumor will grow, and even if and how it will metastasize. There have been other math models that look at tumors, but this one is different. Instead of looking at each cell or all of the cells has a big group, this model creates a kind of patchwork quilt of areas of the tumor to examine. As a result, the doctor can create a tailored plan for treating the disease that is very specific for each patient. The promise is that with specialized (rather than generalized) treatment plans will offer patients a better chance at survival.

Treating Acetaminophen OverdosesWhen a patient comes into the emergency room having overdosed on acetaminophen, the ER staff is faced with a really complex decision. Often these patients are hallucinating, unconscious or comatose. And since it’s relatively easy to overdose on the drug (it takes only five times the daily safe dosage, and acetaminophen is in many different over-the-counter and prescription medications), it’s sometimes impossible to determine when and how much of the drug was ingested. There is an antidote, but at a certain point, the doctor needs to skip that step and put the patient on the liver transplant list immediately. The trick is accurately identifying that point. University of Utah mathematician, Fred Adler, developed a set of differential equations that can better pinpoint the critical information needed to make these decisions.

In both of these cases, the math is pretty darned complicated, depending on a branch of calculus called differential equations. This approach is a step up from statistical analysis, which compares patient data to data collected from other patients. In other words, it assumes that tumors grow in the same way in all patients — which we know isn’t true. These dynamical math approaches allow doctors to offer treatments that are customized for each patient, based only on the information collected from the patient.

And the best part is that the doctors don’t have to know the math. If future studies bear out these new discoveries, a simple app can be designed for smart phones or tablets, allowing physicians to make diagnoses and treatment plans bedside.

I suspect these applications will continue to grow, as the medical community turns to mathematicians for insight into what we can’t see. That’s great news, because these advances can save lives.

I hope you’ve enjoyed what we’ve put together here for Math Appreciation Month. If you have questions, please ask them below. I’m always open to ides for future blog posts, so please share them!

Photo courtesy of fotosinteresantes

Math and cancer?  Turns out the queen of sciences can actually help doctors treat cancer in individual patients.  I looked at a particularly important study by researchers at the University of Miami and University of Heidelberg for Healthymagination, a GE-owned website that addresses health topics.

In short, researchers developed a math model to predict the growth of individual tumors in individual patients.  This is different from previous models that used statistical analysis of how tumors typically grow.  The results also predict whether or not the tumor will metastasize.

The results? Much more reliable diagnoses and treatment plans.  That’s good news for everyone.

Read my guest post here.

Do you have questions about math modeling?  Ask in the comments section.