Mathematical models make it possible to predict the effect of drugs and medical treatments
By Professor Tzvia Egor, Scientific American
Biomathematics, a relatively new scientific field that analyzes biological phenomena using mathematical models, began to develop in the second half of the twentieth century. His goal was to study the complexity of biological processes. My work in this field is based on the assumption that the same laws underlie the dynamics of different biological systems at different levels of organization. For example, mathematical formulas that describe the growth rate of rabbit populations should also correspond to the description of the growth of cancer cell populations.
Experimental biologists working at the cellular level, for example, are developing analytical tools that are essentially similar to a camera in the photographic world. They are able to see the microscopic world they are exploring as a collection of images. On the other hand, biomathematical formulas, for example those that describe intracellular biochemical pathways, actually give a dimension of movement to the images and allow us to observe the dynamics of the world we study. In addition to the fact that such a "film" has more information than a series of images, it also allows the scientist to study the system more accurately and efficiently. Biomathematics allowed me to develop and test new theories dealing with improving cancer treatment in a way that is not possible with experimental biology "of pictures".
In the 80s I used principles from the field of population biology to develop relatively simple formulas describing the growth of mixed populations of healthy cells and cancer cells. The analysis of these formulas led to the proposal to adopt new medication regimens that would significantly reduce the toxicity of chemotherapy treatment. With the help of mathematical tools, we were able to prove, in this case, the universality of the theoretical results, that is, their general validity. Today, our research in the company I founded, Optimata, is the first of its kind to succeed, through sophisticated mathematical models, in making accurate quantitative predictions of the effect of medical treatment on the patient.
During my research I came to know that biomathematical methods can be of great help to doctors in the decision-making process. This recognition led to the founding of Optimata, where we developed sophisticated software known as the "virtual patient". This software can help doctors and drug developers identify improved drug regimens for patient care. With the help of this commercial company, which is currently conducting large-scale clinical tests of the virtual patient, we hope to succeed in transforming the fields of medicine and drug development from fields based on trial and error to fields based on scientific predictions.
In the coming months, we hope to achieve positive results in the initial large-scale clinical trials currently underway in hospitals in Europe and Israel. These tests examine the ability of our technology to accurately predict the toxicity of various drugs and their effect on the progression of breast cancer. Our hope is that eventually every doctor and every hospital will use this technology to test different treatments for patients. Meanwhile, it can be used by drug developers to streamline the development process.
Our technology consists of three main parts (modules). The central part is the virtual patient in whose body a disease develops which is treated with the help of drugs. The virtual patient also reacts with physiological reactions to the drug treatment. As a result, a realistic simulation of the biological and pharmacological processes expected to occur in the patient's body or in a patient population is obtained. Doctors or drug developers can test the accuracy of the resulting forecast.
The second part of the technology makes it possible to identify variables characteristic of different patients, thus adapting the virtual patient to a personal description of different patients or different patient populations. And the third part, and perhaps the most exciting, is a tool that we developed that allows identifying the most effective treatment for each patient according to the requirements of the doctor or the developer of the drug.
By developing the mathematical model that describes the progression of a disease, it is possible to simulate the effect of a drug on the development of the disease and to predict the effectiveness of the drug in a variety of dosage regimens in different patients or patient populations. This makes it possible to calculate the chance that a potential drug treatment will succeed in curing a disease or at least curbing it. By helping drug developers, we are able to assess the expected effectiveness of any drug in humans even in the pre-clinical development stages. When the drug moves to the clinical testing phase, we are able to compare its effectiveness with that of competing drugs already on the market, to assess the feasibility of the development. And perhaps the most important of all, we are able to improve the ratio between the drug's effectiveness and its toxicity in a way that is adapted to different patients.
We believe that awareness of this type of technology is increasing in the pharmaceutical industry. For example, we have already been able to decipher the causes of the toxicity of a drug that at one point was denied approval for distribution by the US Food and Drug Administration (FDA), because the manufacturer was unable to explain the source of the toxicity. In another case, the development of another drug was stopped because it caused an immune response, and we showed that this problem can be overcome if the drug is given at a different dose and timing. Pharmaceutical companies turn to us to help them improve substances that are candidates for use as drugs before moving from animal experiments to clinical trials in humans.
In the field of tailoring the treatment personally to each patient, we receive the initial information about the patient from routine tests performed when she or he is first hospitalized. We feed this information to the computer, which processes data such as sex, age, tumor diameter, presence of metastases or biological markers and turns them into variables that will be fed to the virtual patient (which is actually a kind of virtual clone of the particular patient). That is, we take real information, flesh and blood, to build the virtual patient. After the doctor has entered therapeutic endpoints into the software, that is, desired results of the treatment, the virtual patient software checks various treatment options and produces recommendations for the doctor. Doctors are therefore offered a convenient way to use accurate calculation methods while making clinical decisions, and therefore we hope to be an integral part of the medical care system in the future.
Mathematical models can also affect other fields such as medical devices, genetic diagnostics or other interesting fields. For example, in the field of proteomics (the series of proteins expressed in different cells in different tissues) there are currently several computer technologies that analyze pathological cellular processes. The combination between the sophistication of the field of proteomics and mathematical models of diseases can help doctors simulate unique variables in patients receiving some kind of drug treatment and improve our ability to predict the progression of diseases. Also, today it is possible to produce an accurate genetic profile of a patient, with the help of existing methods known as genetic fingerprinting. Entering this information into the software that describes the complex processes occurring at different levels of organization in the real patient's body will improve the predictive ability of the virtual patient's software.
Professor Tzvia Egor, the chairman and chief scientist of Optimata (www.optimata.com), is a well-known biomathematician who has contributed greatly to the fields of disease theory, chemotherapy optimization and vaccine policy. Professor Egor is also the founder of the Institute for Medical Biomathematics (IMBM), served as the president of the Israeli Society for Theoretical and Mathematical Biology, was a member of the board of trustees of the European Society for Mathematical Biology, and serves as the editor of many scientific journals. Her innovative and original work won her many awards, was published in leading scientific journals and earned her international recognition. Professor Egor received her doctorate from the Hebrew University of Jerusalem and the Free University of Brussels.
The article is presented at the initiative and with the assistance of Bernard Dichek, editor of www.bioisrael.com, an online magazine dealing with the Israeli life sciences industry.
Scientific American website in Hebrew where you can purchase a subscription to the journal
https://www.hayadan.org.il/BuildaGate4/general2/data_card.php?Cat=~~~457355360~~~82&SiteName=hayadan
