I became obsessed with mathematics and physics when I was a junior in high school. Those were the two subjects which I spent most of my time studying. Many of my friends and classmates studied for the sake of passing the exams and unlike me, I was intrigued with applications and tried to find ways to make connections between the two subjects and relating them to the real world. I often wondered if mathematics was meant to be discovered by humans or could it be just a pure invention. I was the kind of student who would spend as much time as needed on the homework in order to develop a complete, in-depth understanding of the subject matter and in so doing, I was quite proficient ( even at that age) to assist other classmates with their assignments. Most of them just wanted the answers to get it done while I focused in explaining the theories and interpreting the meaning of the answers to them. This is the only way I could learn for myself and memorizing formulas alone just didn’t work for me as I found it to be incomplete and dull. I often go beyond what was required of the textbooks and independently made use of outside reference to master the troublesome concepts of the subject matter so I could carry out active discussions with my teachers after school . I guess you could say I was a “math geek” or “science freak” and many of my friends made fun of me ( not in a bad way as they continued to seek my readily offered assistance on a regular basis with their homework), so they had to be somewhat nice to me. I remember to this day that some of the questions they asked me: ” David, you spend so many hours writing mathematical equations, computing probabilities, solving physics problems, and what are you going to do with it in the future? What can you possibly get out of it? What about real life? Can all of those equations apply to real life?” As a teenager, I really didn’t have any answers to those questions and I was completely defenseless. All I knew was that I needed to do well in school, and I would love to find answers to all of those questions, but I couldn’t at the time. At the end, it has taken me close to 30 years to gather the necessary information, and if I knew back then what I know now, I can only become much smarter today. It is never too late and not to mention that learning is an endless journey. We need to update our beliefs as new information comes in, and based upon what we knew in the past, these updates will allow us to have a better understanding of the world, and our knowledge will become more reliable. ( Bayesian science) This triggered my thought and motivated me to writing this blog. ( Memorial Day Blog).
Cancer is the second leading cause of death in this nation. Just 20 years ago if I told you I could predict with miraculous precision where a tumor will be growing and also predict how long the patient will be able to live under different treatments, you would think I must be under the influence of some sorts and escorted me out of the room. With today high power computers and the sophisticated software which often involve the use of mathematical equations as models in the program to carry out simulations, we can take into account how fast tumors divide and disperse through tissues and predict the path. These days it takes perhaps several hours to run a patient’s data through simulations to predict cancer progression in patients including those who are under treatments. Mathematicians, engineers, and medical physicists are constantly trying to develop new precision to the science of cancer treatment. In a nutshell, their work involve inputting scanned data, pathology scores, or gene test results into mathematical equations serving as models in order to calculate the rate of the spread of tumor within the patient. These are the technological development from evolutionary biology, chemical engineering, and high energy nuclear physics. The main task is to capture tumor complexity using mathematical equations and a good example of such equation resembles Fourier heat equation. ( if you have taken a course in partial differential equation.) So we gather data from patients, feed them into mathematical equations and run the simulations through a fast computer to get a reliable prediction of what will happen, very much like risk assessment industry in a nuclear or chemical power plant where they have to perform simulations of various possible disasters and implement safety recommendations and policies. When it comes to cancer therapy, it is almost never a one-size-fits-all therapy, but personalized treatments, maximizing efficacy and minimizing side effects.The biggest obstacle in any cancer therapies is the number of mutations involved. ( Thanks but no thanks to evolution.) Large number of gene alterations involved with each type of cancer is immense,( 1007 in pancreatic cancer alone.) The growth of tumors are also affected by blood supply and immune system. Scientists are battling with understanding the mechanism of these mutations and what causes certain types of tumors to spread and relocate in different areas to multiply. The National Cancer Institute spends millions of dollars every year in virtual cancer work and so do Biotech firms. Mathematical models are also very effective in aiding drug developers to sort through tumor promoting proteins much faster and determine which drug works better depending on the patient’s condition and the type of cancers including the progression of the tumor within the patient. We are in desperate need of a method to distinguish which mutations are driving the growth and how to control it. There is a special branch of mathematics known as catastrophe theory which examines what causes tumors to come back after responding to chemotherapy, and I believe as of now, they are testing it on animals such as mice. Computers and mathematics are helping to design new cancer vaccines and all the quantitative calculations reveal that simple vaccine given at the right moment could bolster the immune system, so timing considerations cannot be ignored. When it comes to medicines, especially cancer treatments, nobody can undermine the importance of mathematics and science. These mathematical models are not only applicable in real life, but they can save lives as well. I wish I knew this when I was in high school so I could easily defend myself and showed how critical it is for people to understand and develop all the necessary mathematical equations in various cancer therapies.
So what about physics? What role does it play in the real world of medicines? I have taught particle physics for more than 10 years and I often put strong emphasis on cancer therapies. Convention X ray radiation therapy revolutionized cancer treatment back in the late 60’s to mid 70’s making use of radium 88 or cobalt 60. However, x-ray releases energy on its way to the tumor and therefore can be very harmful to surrounding tissues. These x-ray beams are composed of primary photons and secondary electrons and deliver radiation to healthy tissues before and after the tumor site. It may cause severe damage to normal tissue or organs near the tumor area. Now think of a 400000 lb cancer-destroyer device which is capable to target a patient’s tumor with an incredible precision down to the millimeter scale while sparing nearby healthy tissues but at the same time, it minimizes side effects. This is the major breakthrough of cancer therapy and that’s proton therapy.
Since no two persons will ever have exactly the same size and shape of a tumor, the advantage of proton treatment is that it is a conformal therapy meaning a customized treatment in which the physician can control and structure the proton beam to the exact size and shape of the tumor where the proton releases the bulk of its cancer-fighting energy.. As the protons move through the body, they slow down and interact with electrons and release energy. The point where the highest energy release occurs is the “Bragg peak” causing the most damage to the targeted tumor cells. In a nutshell, the proton beam conforms to the size, shape and depth of the tumor while sparing healthy tissues and organs. The way it works is very similar to a particle accelerator. First of all, the protons are injected into a linear accelerator and then into the synchrotron where the protons are accelerated to gain more energy. The delivery of the proton beams is controlled by a network of computers with a gantry that can revolve 360 degrees, permitting the beam to be delivered at any angle and to the depth of the tumor. There are medical physicists on the team and they are specialized in formulating mathematical models and crunching out numbers such as the required velocity of the beam in order to be delivered to the right location and the depth of the tumor. Protons release most of the energy when they reach the tumors and so a much higher dose can be used during the treatment. At maximum energy, a proton beam can travel at two-thirds the speed of light, namely 125,000 miles per second. A significant power of proton therapy is that higher doses of radiation can be used to control and manage cancer while reducing damage to surrounding healthy tissues and vital organs. Proton radiation has a very short life span inside the patient’s body. Many patients are able to leave the treatment room immediately after the treatment without any risks and resume to their normal daily activities. In conclusion, proton therapy is made possible because of the advancement in mathematical modeling and computer technology, meaning mathematics and physics as a combined creative agent for this major breakthrough therapy.
When it comes to science and mathematics, I often tell my college students that it isn’t my job to make them fall in love with the subject matters and reach to the same passionate level as I do, but to make an impression upon them to develop a sense of appreciation for mathematics and science, realizing that even if they are not involved with any of the scientific work in their careers, it will continue to have an impact in their lives. The quality of their lives will only get better with further development in science without the need of KARMA. Natural science by its very nature is to help us get a better understanding of how things work based on what we see around us every day. However, there are always new information coming in and so we have the obligations to update our beliefs and making our knowledge somewhat more reliable. It can only get better, not worse. As a scientist, I speculate based on observations, describe with mathematical equations, await for data to supporting the theory, and last but not least, update as new information is available, making our theories better and better. This is truly an evolutionary process in science. In today medical field, we are definitely witnessing this evolutionary trend and it will continue to evolve to improve the quality of our living.