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Text Chapter 767 [Mathematical Models and Equations 5] Combination of Two and Three

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    "For mathematicians, all problems in the world are mathematical problems, and all phenomena in daily life can be explained by mathematics I am a doctor, but what I once loved most was mathematics. All of my  I believe that mathematics can be used to treat diseases, even cancer"

    Kristen *Kyle talked eloquently, with confidence written all over her face. Even these old experts and old otakus had to secretly praise, "It's so cool!"  ¡¯

    In fact, her job is really cool. She is the director of the Cancer Research Office of the Royal Swedish Academy of Medicine, and her research direction is unique - using mathematics to study cancer.

    "Is there mathematics to treat diseases? Did I hear you correctly? Am I crazy or is this woman crazy?"

    "Are you going to throw out the theory of mathematical omnipotence again? Whose conjecture is it this time"

    "Forget it, for the sake of Director Jay Chou and the Zhou Group, just listen to what she has to say."

    Needless to say, Ye Decao, Zhang Gongzi, Wei Minghe and other domestic first-class experts and scholars, the rest can join the project team. Which one is not a famous figure in the medical field?  And all of them have more than ten or even decades of experience in cancer research.  Generally speaking, if the world's medical community has any breakthroughs or new theories in cancer research, they will know it immediately. Before Kyle immersed himself in studying her 'mathematical treatment theory', he was still very productive in the field of cancer research.  Countless, some experts have heard of her name; however, Christine Kyle will be disappointed this time. Since she started theoretical research on mathematical treatment of cancer, she has been laughed at by many so-called mainstream scholars even in Europe.  Gradually, it no longer attracts the attention of the world's medical community, and some research results are rarely published in influential medical journals. How could these old experts and otakus in China know about it? Naturally, they were in an uproar, thinking that this woman was really crazy.

    Looking at the colleagues in the audience who were either snickering or looking disdainful.  Christine Kyle straightened out her chest, making her already tall front look even more straight.

    She has her persistence. In 21, her father died of lung cancer when she was a graduate student in the Department of Applied Mathematics.  It was an extremely difficult time.  Her father is an engineer, and all her knowledge and hobbies in mathematics come from his father. He played mathematical games with her when she was young, cultivating her thinking habit of quantitatively analyzing everything.  After her father passed away, she chose to enter medical school, where her research direction was mathematical biology.  He studied under the famous professor of neuropathology Ellsworth Allward, specializing in brain cancer.  The reason why she did not choose to start with lung cancer was because cancer was too difficult for her to face. Her two brothers also died of lung cancer inexplicably. This was like a family block that made her dream about it at midnight.  Breaking out in a cold sweat.

    Mathematics may not explain fate, but it can at least explain cancer, for that matter.  She believed it.

    "A naive researcher, with a crazy idea to save the world, hopes to use mathematics to solve the world's biggest problems." She once said to her supporters with a smile, "It was very cold water at the time. Even today.  If you say that cancer is manageable and predictable, you will still be met with skepticism or even ridicule. This skepticism is reasonable; the mechanism of cancer occurrence and metastasis is too complex. How can so much molecular data be simplified into  How about a few mathematical formulas? But I have to do it!"

    Not long ago.  Christine Kael published an article in Cell, a small Swedish medical journal, exploring what went wrong in humanity's war on cancer.

    She concluded that one cancer cell is smarter than 100 top cancer experts.  As humans learn more about cancer.  It turns out that cancer is more complicated than expected.  They invade the immune system, travel across blood vessels, colonize distant organs, and recruit normal cells to support their rebellion¡­

    Molecular biology research has discovered more than 25,000 genetic mutations related to cancer, and this number is still increasing.  A recent study by Johns Hopkins University in the United States showed that pancreatic cancer alone involves 1,007 different genetic mutations.  In addition, the growth of cancer cells is also affected by the surrounding blood supply, nutrition and immune system status.

    From a "war" perspective, the addition of mathematicians is undoubtedly a powerful foreign aid.  In fact, as early as 50 years ago, mathematicians had tried to use mathematics to explain cancer, but decades have passed before this type of research entered the mainstream medical field from obscure academic journals; finally, it came to the biology of cancer.  When scientific data accumulated at an alarming rate, and the entire medical community was in urgent need of quantitative tools to organize and analyze these data, Christine Kyle knew that her opportunity had come.

    "Right now, the entire cancer research is focused on the molecular biology level: genes, intracellular signaling pathways, and most recently, microRNAs. The financial resources of the entire country, and even the world, are focused on small genetic mutations. The question is, how do we  Link these micro-level data and information to a specific patient's tumor.?¡±

    Christine Kyle gently pushed up her gold-rimmed glasses. Her proud figure, beautiful face, and figure that could still be called a 'devil' after nearly forty years old made these old otakus stop unconsciously.  Discussions and ridicules, some looking up at her blankly, I have to say that this is a very charming and intellectual beauty, and the theory she proposed seems quite attractive; of course, if it were Ye Decao on the stage,  People like this old man, a big-mouthed guy who can't describe it, are not in the mood to understand the so-called mathematical methods.

    "They were finally willing to listen to me patiently. My personal beautician was right. A woman's proper display of charm will make many things easier"

    Thinking of this, Christine Kyle glanced at Zhou Yi in the audience, and suddenly became inexplicably interested in the chairman of the Zhou Group and the discoverer of cancer factors. However, this little idea was soon revealed.  The serious atmosphere in front of her faded away. She took a deep breath and began to sort out what she wanted to express. She only had one chance. She had to conquer the young chairman and the old guys in the project team and make them agree with her research results.  In order to achieve results join this project team.

    "Using mathematics to treat cancer sounds incredible Well, let's choose an angle that everyone can accept"

    Christine Kyle gave all the experts present a very sure, confident, and conquering look, just like a high-ranking queen giving a speech to her people: "My idea is to jump out of the molecular level.  Let¡¯s start from the perspective of clinical imaging. After all, this is the most commonly used and most visual monitoring method by doctors. It directly affects the patient¡¯s diagnosis and treatment process"

    "The problem with current clinical imaging is that it cannot detect all tumors. Many cancer cells are hidden under the water. This means that when doctors understand the patient's tumor, a lot of information is lost. Not only is it impossible to remove with surgery,  For all tumors, other treatment modalities are also limited. So, I want to design a model that allows doctors to see the situation "under the deep water". Of course, this is a mathematical model"

    The beginning is always the hardest, but once you get into the zone.  She, the speaker, and the audience were soon drawn into her mathematical world together.

    Christine Kyle¡¯s main research focus is brain glioma.  This is the most common type of malignant brain tumor and the most dangerous because it spreads very quickly.  It is like a hand that slowly stretches out in the mind. When it is diagnosed, it is often accompanied by hundreds of genetic mutations, and clinical imaging detection equipment such as MRI (nuclear magnetic resonance) can only reveal the tip of the iceberg, 99.9% of cancer cells.  It cannot be displayed.

    This kind of brain tumor does not conflict with the "human brain immortality theory" that Zeng Ming insisted on before. The so-called human brain by Zeng Ming and others is actually no longer a physical brain.  It is an abstract human brain that contains the concepts of spirit and soul. However, despite this, Zeng Ming was very interested in her speech and listened very carefully.

    Her model is actually a set of partial differential equations.  Based on a patient's m-day historical data, the speed at which cancer cells divide and spread within the brain tissue is calculated, and its diffusion path is simulated. It not only displays the current true distribution of cancer cells in the brain (including the invisible parts of the m-day).  It can also calculate the location and speed at which it is most likely to invade next.

    It can accurately predict how long a patient will live, rather than giving a general "median survival period", and more importantly.  It can predict a patient's response to and effectiveness of radiotherapy.  According to the current standard procedure, a brain cancer patient must receive brain radiation therapy once every six weeks, which is often accompanied by serious side effects. But her model shows that some patients whose tumors progress slowly can achieve the same effect by reducing the number of radiation therapy sessions.  , and some patients with rapidly progressing tumors are suitable for low-dose radiotherapy two or three times a day to improve survival.

    Another benefit of this model is that it can prevent patients from attempting dangerous, hopeless and expensive surgeries.  Brain surgery carries high risks and can cause paralysis, affect vision or the ability to speak.  Sometimes, no treatment is the best treatment, which can save a lot of unnecessary pain.

    For a cancer patient, the standardized treatment plan is a cruel and helpless choice.  They often have to take many detours to find a right treatment plan, and by the time they find it, they may not have much time left. On the contrary, if this time is not wasted, the patient may be able to do something more interesting and enjoy life.  Good food, enjoying family relationships

    This is the current reality of medicine - it has never existed for individuals.  However, Christine Kyle¡¯s mathematical model proves that personalized treatment does not have to wait until scientists decipher all the genetic codes before it can be launched. With current technical means, although it is difficult to cure cancer, it can at least maximize the effect.  Reduce harm to patients.  And this mathematical modelThe establishment of ?? can more efficiently help cancer researchers achieve the goal of conquering cancer. For example, the experts and scholars in the audience who were blushing just now because of the dispute over the 'route' are all listening to her speech carefully at this moment;  Whether they're looking at her research results or her towering breasts, Kristen Kyle considers them a success.

    "If you look at patients as a whole, you will find that everything is irregular. The same cancer may have completely different growth and spread patterns in different patients. But from an individual point of view, in fact, the cancer in each patient  Cells, whose growth and spread patterns are traceable, can greatly reduce the difficulty of conquering cancer."

    Opening her laptop and connecting it to the projector, Christine Kyle began to show her research results.  In fact, her mathematical model is very simple, with only two key parameters, but the prediction results are surprisingly accurate, and have been verified on more than 1,350 patients.

    ¡°Mathematics has amazing predictive power.¡±

    Christine Kyle strives to make her voice more feminine, pleasing these old guys while gaining more time and opportunities to promote her research: "Let's imagine the weather forecast. If in the future  There is such a model. As long as a patient's data is input, regardless of m-day or genetic test results, it will automatically analyze the behavior pattern of the tumor, simulate how the tumor grows, spreads, and metastases, predict the patient's prognosis, and calculate the best drug combination.  And treatment plans. By then, 1,000 patients will have 1,000 different treatment plans. We will be able to completely abandon those stereotyped and rigid treatment procedures. In fact, they have never been scientific."

    "Also, I boldly make an idea. If everyone can accept my research results, maybe it will reduce everyone's debates and make the disputes between schools disappear invisible in the face of great mathematics?"

    Christine Kyle's Chinese literature is really great. After hearing this, even Zhou Yi nodded unconsciously. Cheng Dong is very capable. This female medical scientist appeared too timely.

    Christine Kyle¡¯s proposal isn¡¯t just a nice idea.  In fact, some mathematical models have provided possible answers or even solutions to some practical problems that have troubled doctors for many years.  for example.  What level of chemotherapy is beneficial to patients?  Researchers at the University of Virginia in the United States once used cancer genetic analysis to design a mathematical model to predict the effectiveness of the same chemotherapy drug on different patients with an accuracy of up to 85%.  This model has been validated in bladder and breast cancer and has the potential to be applicable to all cancer types.  It will soon enter clinical trials.

    When doctors face an early-stage cancer patient, the first question is often: How aggressive are the cancer cells?  Is the probability of transfer high?  Does the patient need aggressive treatment, or a milder regimen?  Although m-day and CT can show the size and shape of the tumor, they cannot accurately estimate its potential aggressiveness.  The discovery of mathematical models by Professor Vito of Vanderbilt University in the United States.  The aggressiveness of cancer cells is not only due to the genetic mutation itself, but the surrounding microenvironment also determines its composition and aggressiveness, as long as one of the variables is changed.  For example, oxygen content can adjust the aggressiveness of tumors.

    The "nonlinear scheduling algorithm" (an "optimization algorithm" that seeks the highest efficiency among thousands of variables and constraints) proposed by the Ukrainian mathematician Roman 25 years ago was recently used by German researcher Lembert.  Calculate the angle, intensity, and duration of radiotherapy rays to destroy tumors with maximum efficiency without damaging healthy tissue at the edges.  This system has been used in radiotherapy departments of some hospitals in Germany.

    What is even more exciting is the chronic myelogenous leukemia (CML) model of Doron Levy, a professor in the Department of Applied Mathematics at the University of Maryland.  CML is the "simplest" cancer because it involves only a single genetic mutation.  In 2001, after the invention of a targeted drug called Gleevec, the five-year survival rate of patients with chronic leukemia increased from 50% to 95%.  But the problem is that patients must rely on Gleevec for a long time. Once the drug is stopped, the number of cancer cells in the blood will return to the level before treatment, or even higher.  Once a patient develops resistance to Gleevec, the situation becomes dire.

    Professor Doron Levy¡¯s model basically allows the patient¡¯s immune system to replace Gleevec in fighting cancer cells, thereby getting rid of dependence on Gleevec.  He spent 4 years tracking, collecting and analyzing the immune response status of CML patients while taking Gleevec.  Finally, he discovered that when first diagnosed, the patient's immune system was very weak, but once he started taking Gleevec, the anti-leukemia immune response in the patient's body continued to increase, reaching a peak and then slowly falling back.  During this time, the cancer cells are still there, but in relatively small numbers, causing the immune system to become less vigilant.  At this time, a simple cancer vaccine (the patient's blood at the early stage of diagnosis is injected back into the patient's body after killing the cancer cells) can reactivate the immune system.  ThisThe key to the model is to calculate the best time to inject the vaccine for the patient. The immunotherapy program guided by it is likely to eventually cure leukemia.

    Of course, these results have not entered the mainstream medical field. Even Zhou Yi had a certain understanding after reading the information that Christine Kyle brought with her.  The experts and scholars present, including senior fellow apprentice Ye Decao and General Cheng Dazuicheng, all had their eyes wide open and were almost conquered by her.

    There are a thousand treatments for a thousand patients?  Then what are we arguing about? Aren¡¯t we all like children playing house, and playing around is childish?  It hurts my self-esteem so much But I have to admit that this woman not only has big breasts, but also has a high IQ!

    Standing up, Zhou Yi applauded vigorously: "What a great talk, Dr. Kyle. You are an excellent medical scientist and an amazing mathematician! I want you to join the project team. No one else  I will object" (To be continued)
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